an exact algorithm for the pallet loading problem abstract the two dimensional packing problem of finding optimal layouts for identical rectangular boxes on a rectangular pallet has interested or practitioners for many years the problem is np complete and solution methods to date tend to be heuristic this paper discusses the development of an exact tree search algorithm based on a graph theoretic model of the problem

a spectral sequence for polyhedral products abstract the purpose of this paper is to exhibit fine structure for polyhedral products z k x a and polyhedral smash products z k x a where moment angle complexes are special cases in which x a d 2 s 1 there are three main parts to this paper 1 one part gives a natural filtration of the polyhedral product together with properties of the resulting spectral sequence in theorem 2 15 applications of this spectral sequence are given 2 the second part gives a homological decomposition of z k x a in case x a consists of cw pairs by using part 1 3 applications to the ring structure of z k x a are given for cw pairs x a satisfying suitable freeness conditions

local torus actions modeled on the standard representation abstract we introduce the notion of a local torus action modeled on the standard representation for simplicity we call it a local torus action it is a generalization of a locally standard torus action and also an underlying structure of a locally toric lagrangian fibration for a local torus action we define two invariants called a characteristic pair and an euler class of the orbit map and prove that local torus actions are classified topologically by them as a corollary we obtain a topological classification of locally standard torus actions which includes the topological classifications of quasi toric manifolds by davis and januszkiewicz and of effective t 2 actions on four dimensional manifolds without nontrivial finite stabilizers by orlik and raymond we discuss locally toric lagrangian fibrations from the viewpoint of local torus actions we also investigate the topology of a manifold equipped with a local torus action when the euler class of the orbit map vanishes

equivariant basic cohomology of riemannian foliations the basic cohomology of a riemannian foliation on a complete manifold with all leaves closed is the cohomology of the leaf space in this paper we introduce various methods to compute the basic cohomology in the presence of both closed and non closed leaves in the simply connected case or more generally for killing foliations we show that the total basic betti number of the union c of the closed leaves is smaller than or equal to the total basic betti number of the foliated manifold and we give sufficient conditions for equality if there is a basic morse bott function with critical set equal to c we can compute the basic cohomology explicitly another case in which the basic cohomology can be determined is if the space of leaf closures is a simple convex polytope our results are based on molino s observation that the existence of non closed leaves yields a distinguished transverse action on the foliated manifold with fixed point set c we introduce equivariant basic cohomology of transverse actions in analogy to equivariant cohomology of lie group actions enabling us to transfer many results from the theory of lie group actions to riemannian foliations the prominent role of the fixed point set in the theory of torus actions explains the relevance of the set c in the basic setting

the ring structure on the cohomology of coordinate subspace arrangements every simplicial complex delta subset2 n on the vertex set n 1 ldots n defines a real resp complex arrangement of coordinate subspaces in mathbb r n resp mathbb c n via the correspondence delta ni sigma mapsto rm span e i i in sigma the linear structure of the cohomology of the complement of such an arrangement is explicitly given in terms of the combinatorics of delta and its links by the goresky macpherson formula here we derive by combinatorial means the ring structure on the integral cohomology in terms of data of delta we provide a non trivial example of different cohomology rings in the real and complex case furthermore we give an example of a coordinate arrangement that yields non trivial multiplication of torsion elements

algebraic invariants for right angled artin groups a finite simplicial graph determines a right angled artin group g with generators corresponding to the vertices of and with a relation w w for each pair of adjacent vertices we compute the lower central series quotients the chen quotients and the first resonance variety of g directly from the graph

the uniqueness of the integrated density of states for the schrodinger operators with magnetic fields the integrated density of states ids for the schrodinger operators is defined in two ways by using the counting function of eigenvalues of the operator restricted to bounded regions with appropriate boundary conditions or by using the spectral projection of the whole space operator a sufficient condition for the coincidence of the two definitions above is given moreover a sufficient condition for the coincidence of the ids for the dirichlet boundary conditions and the ids for the neumann boundary conditions is given the proof is based only on the fundamental items in functional analysis such as the min max principle etc

the absolute continuity of the integrated density of states for magnetic schrodinger operators with certain unbounded random potentials the object of the present study is the integrated density of states of a quantum particle in multi dimensional euclidean space which is characterized by a schrodinger operator with magnetic field and a random potential which may be unbounded from above and below in case that the magnetic field is constant and the random potential is ergodic and admits a so called one parameter decomposition we prove the absolute continuity of the integrated density of states and provide explicit upper bounds on its derivative the density of states this local lipschitz continuity of the integrated density of states is derived by establishing a wegner estimate for finite volume schrodinger operators which holds for rather general magnetic fields and different boundary conditions examples of random potentials to which the results apply are certain alloy type and gaussian random potentials besides we show a diamagnetic inequality for schrodinger operators with neumann boundary conditions

the polyhedral product functor a method of decomposition for moment angle complexes arrangements and related spaces this article gives a natural decomposition of the suspension of generalized moment angle complexes or partial product spaces which arise as polyhedral product functors described below the geometrical decomposition presented here provides structure for the stable homotopy type of these spaces including spaces appearing in work of goresky macpherson concerning complements of certain subspace arrangements as well as davis januszkiewicz and buchstaber panov concerning moment angle complexes since the stable decompositions here are geometric they provide corresponding homological decompositions for generalized moment angle complexes for any homology theory

homotopy groups of k contact toric manifolds contact toric manifolds of reeb type are a subclass of contact toric manifolds which have the property that they are classified by the images of the associated moment maps we compute their first and second homotopy group terms of the images of the moment map we also explain why they are k contact

equivariant cohomology distinguishes toric manifolds the equivariant cohomology of a space with a group action is not only a ring but also an algebra over the cohomology ring of the classifying space of the acting group we prove that toric manifolds i e compact smooth toric varieties are isomorphic as varieties if and only if their equivariant cohomology algebras are weakly isomorphic we also prove that quasitoric manifolds which can be thought of as a topological counterpart to toric manifolds are equivariantly homeomorphic if and only if their equivariant cohomology algebras are isomorphic

on the difference between real and complex arrangements if b is an arrangement of linear complex hyperplanes in c d then the following can be constructed from knowledge of its intersection lattice a the cohomology groups of the complement br b the cohomology algebra of the complement os c the fundamental group of the complement if d 2 d the singularity link up to homeomorphism if d 3 e the singularity link up to homotopy type zz if bis more generally a 2 arrangement in ir 2d an arrangement of real subspaces of codimension 2 with even dimensional intersections then the intersection lattice still determines a the cohomology groups of the complement gm and e the homotopy type of the singularity link zz we show however that for 2 arrangements the data b c and d are not deter mined by the intersection lattice they require the knowledge of extra information on sign patterns which can be computed as determinants of linear relations or equiva lently as linking coefficients in the sense of knot theory

coincidences between homological densities predicted by arithmetic abstract motivated by analogies with basic density theorems in analytic number theory we introduce a notion and variations of the homological density of one space in another we use weil s number field function field analogy to predict coincidences for limiting homological densities of various sequences z n d 1 d m x of spaces of 0 cycles on manifolds x the main theorem in this paper is that these topological predictions which seem strange from a purely topological viewpoint are indeed true one obstacle to proving such a theorem is the combinatorial complexity of all possible collisions of points this problem does not arise in the simplest and classical case m n 1 2 of configuration spaces to overcome this obstacle we apply the bjorner wachs theory of lexicographic shellability from algebraic combinatorics

the minimum size instance of a pallet loading problem equivalence class abstract the pallet loading problem plp maximizes the number of identical rectangular boxes placed within a rectangular pallet boxes may be rotated 90 so long as they are packed with edges parallel to the pallet s edges i e in an orthogonal packing this paper defines the minimum size instance msi of an equivalence class of plp and shows that every class has one and only one msi we develop bounds on the dimensions of box and pallet for the msi of any class applying our new bounds on msi dimensions we present an algorithm for msi generation and use it to enumerate all 3 080 730 equivalence classes with an area ratio pallet area divided by box area smaller than 101 boxes previous work only provides bounds on the ratio of box dimensions and only considers a subset of all classes presented here

splitting multidimensional necklaces the well known splitting necklace theorem of alon n alon splitting necklaces adv math 63 1987 247 253 says that each necklace with kai beads of color i 1 n can be fairly divided between k thieves by at most n k 1 cuts alon deduced this result from the fact that such a division is possible also in the case of a continuous necklace 0 1 where beads of given color are interpreted as measurable sets ai 0 1 or more generally as continuous measures i we demonstrate that alon s result is a special case of a multidimensional consensus division theorem about n continuous probability measures 1 n on a d cube 0 1 d the dissection is performed by m1 md n k 1 hyperplanes parallel to the sides of 0 1 d dividing the cube into m1md elementary cuboids parallelepipeds where the integers mi are prescribed in advance

how to use structural constraints to compute an upper bound for the pallet loading problem abstract during the last twenty years several heuristics have been developed for the pallet loading problem of packing identical rectangles orthogonally into a large containing rectangle upper bound methods are used to verify the optimality of heuristic solutions if these methods fail exact algorithms have to be applied which may require a prohibitive amount of computing time this paper discusses a new upper bound method based on a set of structural constraints for a solution which realizes the assumed upper bound the constraints spring from a linear programming problem which is solved for various cost functions by means of several arguments these constraints can be gradually tightened if this leads to a contradiction then the upper bound estimate was too high and must be decremented this method is shown to be accurate for all but 28 problems in a random sample of 20 000 an improvement of 262 over previous methods

the signature of a toric variety we identify a combinatorial quantity the alternating sum of the h vector defined for any simple polytope as the signature of a toric variety this quantity was introduced by r charney and m davis in their work which in particular showed that its nonnegativity is closely related to a conjecture of h hopf on the euler characteristic of a nonpositively curved manifold we prove positive or nonnegative lower bounds for this quantity under geometric hypotheses on the polytope and in particular resolve a special case of their conjecture these hypotheses lead to ampleness or weaker conditions for certain line bundles on toric divisors and then the lower bounds follow from calculations using the hirzebruch signature formula moreover we show that under these hypotheses on the polytope the ith l class of the corresponding toric variety is 1 i times an effective class for any i

vector bundles over davis januszkiewicz spaces with prescribed characteristic classes for any n 1 dimensional simplicial complex we construct a particular n dimensional complex vector bundle over the associated davis januszkiewicz space whose chern classes are given by the elementary symmetric polynomials in the generators of the stanley reisner algebra we show that the isomorphism type of this complex vector bundle as well as of its realification are completely determined by its characteristic classes this allows us to show that coloring properties of the simplicial complex are reflected by splitting properties of this bundle and vice versa similar questions are also discussed for 2n dimensional real vector bundles with particular prescribed characteristic pontrjagin and euler classes we also analyze which of these bundles admit a complex structure it turns out that all these bundles are closely related to the tangent bundles of quasi toric manifolds and moment angle complexes 2012 american mathematical society

toda lattices with indefinite metric ii topology of the iso spectral manifolds abstract we consider the iso spectral real manifolds of tridiagonal hessenberg matrices with distinct real eigenvalues the manifolds are described by the iso spectral flows of indefinite toda lattice equations introduced by the authors physica d 91 1996 321 339 these toda lattices consist of 2n 1 different systems with hamiltonians h 1 2 k 1 n y k 2 k 1 n 1 s k s k 1 exp x k x k 1 where sk 1 which blow up in finite time except the case with all sksk 1 1 we compactify the manifolds by adding infinities according to the toda flows the resulting manifolds are shown to be nonorientable for n 2 and the symmetry group is the semi direct product of z 2 n 1 and the permutation group s n these properties identify themselves with small covers introduced by davis and januszkiewicz duke math j 62 1991 417 451 as a corollary of our construction we give a formula for the total number of zeros for a system of exponential polynomials generated as hankel determinants

asymptotic expansion for the density of states of the magnetic schrodinger operator with a random potential we study the asymptotics for the density of states of the magnetic schrodinger operator with a random potential by using the methods of effective hamiltonian complex dilation and complex translation we obtain in the large magnetic field limit the asymptotic expansion for the density of states measure considered as a distribution

small rational model of subspace complement this paper concerns the rational cohomology ring of the complement m of a complex subspace arrangement we start with the de concini procesi differential graded algebra that is a rational model for m inside it we find a much smaller subalgebra d quasi isomorphic to the whole algebra d is described by defining a natural multiplication on a chain complex whose homology is the local homology of the intersection lattice l whence connecting the de concini procesi model with the goresky macpherson formula for the additive structure of h m the algebra d has a natural integral version that is a good candidate for an integral model of m if the rational local homology of l can be computed explicitly we obtain an explicit presentation of the ring h m q for example this is done for the cases where l is a geometric lattice and where m is a k equal manifold

analysis of upper bounds for the pallet loading problem this paper is concerned with upper bounds for the well known pallet loading problem plp which is the problem of packing identical boxes into a rectangular pallet so as to maximize the number of boxes fitted after giving a comprehensive review of the known upper bounds in the literature we conduct a detailed analysis to determine which bounds dominate which others the result is a ranking of the bounds in a partial order it turns out that two of the bounds dominate all others a bound due to nelissen and a bound obtained from the linear programming relaxation of a set packing formulation experiments show that the latter is almost always optimal and can be computed quickly

on cohomology algebras of complex subspace arrangements the integer cohomology algebra of the complement of a complex subspace arrangement with geometric intersection lattice is completely determined by the combinatorial data of the arrangement we give a combinatorial presentation of the cohomology algebra in the spirit of the orlik solomon result on the cohomology algebras of complex hyperplane arrangements our methods are elementary we work with simplicial models for the complements that are induced by combinatorial stratifications of complex space we describe simplicial cochains that generate the cohomology among them we distinguish a linear basis study cup product multiplication and derive an algebra presentation in terms of generators and relations

the theory of toric manifolds toric manifolds the topological analogue of toric varieties are determined by an n dimensional simple convex polytope and a function from the set of codimensionone faces into the primitive vectors of an integer lattice their cohomology was determined by davis and januszkiewicz in 1991 and corresponds with the theorem of danilovjurkiewicz in the toric variety case we use the adams spectral sequence to compute the ko theory of all toric manifolds and certain toric varieties

equivariant cohomology and the varchenko gelfand filtration abstract the cohomology of the configuration space of n points in r 3 is isomorphic to the regular representation of the symmetric group which acts by permuting the points we give a new proof of this fact by showing that the cohomology ring is canonically isomorphic to the associated graded of the varchenko gelfand filtration on the cohomology of the configuration space of n points in r 1 along the way we give a presentation of the equivariant cohomology ring of the r 3 configuration space with respect to a circle acting on r 3 via rotation around a fixed line we extend our results to the settings of arbitrary real hyperplane arrangements the aforementioned theorems correspond to the braid arrangement as well as oriented matroids

groups generated by reflections and aspherical manifolds not covered by euclidean space a coxeter system r v is a group r a coxeter group together with a set of generators v such that each element of v has order two and such that all relations in r are consequences of relations of the form vw m v w 1 where v w e v and m v w denotes the order of vw the m v w s which are positive integers or oo obviously determine the coxeter system up to isomorphism the list of finite coxeter groups is short and well known however general coxeter groups are much more flexible in fact the set v and the m v w s can be specified arbitrarily at least if v is finite subject only to the conditions m v v 1 and m v w m w v 2 if v w suppose that r v is a coxeter system that x is a hausdorff space and that xv v v is a locally finite family of closed subspaces indexed by v the xv are called the panels of x 2 there is a classical method for constructing a transformation group from these data for each x e x let v x denote the set of v in v such that x e xv for each subset s of v let rs be the subgroup generated by s and let xs be the face of x defined by

lie algebraic aspects of the finite nonperiodic toda flows in this paper we review various aspects of nonperiodic full and tridiagonal toda flow theory in particular we consider gradient structures in the dynamics and geometry of these systems and we compare and contrast a number of formulations of the nonperiodic toda equations we describe the structure of these systems on general semisimple lie algebras in the case of the full kostant asymmetric toda flow we describe some of the background behind its integrability and explain the role of noncommutative integrability in its qualitative behavior we describe the relationship between the asymmetric toda flows and the symmetric and indefinite toda flows and show how one may conjugate from the full kostant toda flows to the full symmetric toda flows via a poisson map we describe briefly related toda systems such as nonabelian toda and the peakon flows

topological representations of matroids one of the foundations of oriented matroid theory is the topological representation theorem of folkman and lawrence 8 it says that an oriented simple matroid can be realized uniquely as an arrangement of pseudospheres that there is no similar interpretation for the class of all matroids has been taken for granted for instance a non coordinatizable matroid of abstract origin may be thought of as a geometric object only in a purely formal way whereas an oriented matroid may always be thought of as a geometric topological configuration on the d sphere or in projective space 3 p 19 our main theorem is that the class of geometric lattices which is cryptomorphic to the category of simple matroids is the same as the class of intersection lattices of arrangements of homotopy spheres the interpretation of a geometric lattice as an arrangement of homotopy spheres is a natural generalization of the folkman lawrence theorem an oriented matroid realizable over r has a representation with geodesic spheres allowing pseudospheres i e those which are homeomorphic but possibly not isometric to the unit sphere leads to the category of simple oriented matroids if we further relax the conditions on the spheres to only homotopy equivalence to the standard sphere then we are led to the category of all simple matroids some of the theory of oriented matroids which only depends on the underlying matroid can be extended to homotopy sphere arrangements zaslavsky s enumerative theory for pseudosphere arrangements can be extended to the homotopy setting as in the oriented matroid representation theorem the arrangement can be forced to be antipodal so a realization as homotopy projective spaces is also possible the minimal cellular resolutions of orientable matroid ideals developed in 10 can be extended to arbitrary matroids by using arrangements of homotopy spheres our point of view is primarily through the lens of oriented matroids hence the homotopy spheres which represent the atoms of the geometric lattice have codimension one in the future we hope to examine the point of view of complex hyperplane arrangements and consider spheres of even codimension the matroid theory we require is in section 2 while section 3 presents matroid steiner complexes we review a very general theory of arrangements of topological

the homotopy type of the polyhedral product for shifted complexes abstract we prove a conjecture of bahri bendersky cohen and gitler if k is a shifted simplicial complex on n vertices x 1 x n are pointed connected c w complexes and c x i is the cone on x i then the polyhedral product determined by k and the pairs c x i x i is homotopy equivalent to a wedge of suspensions of smashes of the x i s earlier work of the authors dealt with the special case where each x i is a loop space new techniques are introduced to prove the general case these have the advantage of simplifying the earlier results and of being sufficiently general to show that the conjecture holds for a substantially larger class of simplicial complexes we discuss connections between polyhedral products and toric topology combinatorics and classical homotopy theory

homotopy types of subspace arrangements via diagrams of spaces we prove combinatorial formulas for the homotopy type of the union of the subspaces in an affine compactified affine spherical or projective subspace arrangement from these formulas we derive results of goresky macpherson on the homology of the arrangement and the cohomology of its complement the union of an arrangement can be interpreted as the direct limit of a diagram of spaces over the intersection poset a closely related space is obtained by taking the homotopy direct limit of this diagram our method consists in constructing a combinatorial model diagram over the same poset whose homotopy limit can be compared to the original one by usual homotopy comparison results for diagrams of spaces

the integrated density of states in strong magnetic fields we consider three dimensional schrodinger operators with constant magnetic fields and ergodic electric potentials we study the strong magnetic field asymptotic behaviour of the integrated density of states distinguishing between the asymptotics far from the landau levels and the asymptotics near a given landau level

projectivities in simplicial complexes and colorings of simple polytopes for each strongly connected finite dimensional pure simplicial complex delta we construct a finite group pi delta the group of projectivities of delta which is a combinatorial but not a topological invariant of delta this group is studied for combinatorial manifolds and in particular for polytopal simplicial spheres the results are applied to a coloring problem for simplicial or dually simple polytopes which arises in the area of toric manifolds

decompositions of the polyhedral product functor with applications to moment angle complexes and related spaces this article gives a natural decomposition of the suspension of a generalized moment angle complex or partial product space which arises as the polyhedral product functor described below the introduction and application of the smash product moment angle complex provides a precise identification of the stable homotopy type of the values of the polyhedral product functor one direct consequence is an analysis of the associated cohomology for the special case of the complements of certain subspace arrangements the geometrical decomposition implies the homological decomposition in earlier work of others as described below because the splitting is geometric an analogous homological decomposition for a generalized moment angle complex applies for any homology theory implied therefore is a decomposition for the stanley reisner ring of a finite simplicial complex and natural generalizations

real quadrics in cn complex manifolds and convex polytopes in this paper we investigate the topology of a class of non kahler compact complex manifolds generalizing that of hopf and calabi eckmann manifolds these manifolds are diffeomorphic to special systems of real quadrics cn which are invariant with respect to the natural action of the real torus s1 n onto cn the quotient space is a simple convex polytope the problem reduces thus to the study of the topology of certain real algebraic sets and can be handled using combinatorial results on convex polytopes we prove that the homology groups of these compact complex manifolds can have arbitrary amount of torsion so that their topology is extremely rich we also resolve an associated wall crossing problem by introducing holomorphic equivariant elementary surgeries related to some transformations of the simple convex polytope finally as a nice consequence we obtain that affine non kahler compact complex manifolds can have arbitrary amount of torsion in their homology groups contrasting with the kahler situation

solving the pallet loading problem abstract this paper presents new bounds heuristics and an exact algorithm for the pallet loading problem plp plp maximizes the number of boxes placed on a rectangular pallet all boxes have identical rectangular dimensions and when placed must be located completely within the pallet boxes may be rotated 90 so long as they are placed with edges parallel to the pallet s edges the set of all plp instances with an area ratio pallet area divided by box area less than 101 boxes can be represented by 3 080 730 equivalent classes our g5 heuristic finds optimal solutions to 3 073 724 of these 3 080 730 classes and in the remaining 7006 classes only differs from the best known bound by one box we develop three other heuristics that solve another 54 instances finally we solve the 6952 remaining classes with our exact hvz algorithm only a subset of these classes has been solved previously

the cohomology rings of complements of subspace arrangements the ring structure of the integral cohomology of complements of real linear subspace arrangements is considered while the additive structure of the cohomology is given in terms of the intersection poset and dimension function by a theorem of goresky and macpherson we describe the multiplicative structure in terms of the intersection poset the dimension function and orientations of the participating subspaces for the class of arrangements without pairs of intersections of codimension one in particular this yields a description of the integral cohomology ring of complex arrangements conjectured by yuzvinsky for general real arrangements a weaker result is obtained the approach is geometric and the methods are elementary

hyperbolic 4 manifolds colourings and mutations we develop a way of seeing a complete orientable hyperbolic 4 manifold m as an orbifold cover of a coxeter polytope p h 4 that has a facet colouring we also develop a way of finding a totally geodesic sub manifold n in m and describing the result of mutations along n as an application of our method we construct an example of a complete orientable hyperbolic 4 manifold x with a single non toric cusp and a complete orientable hyperbolic 4 manifold y with a single toric cusp both x and y have twice the minimal volume among all complete orientable hyperbolic 4 manifolds

a fast algorithm for identifying minimum size instances of the equivalence classes of the pallet loading problem abstract in this paper a novel and fast algorithm for identifying the minimum size instance msi of the equivalence class of the pallet loading problem plp is presented the new algorithm is based on the fact that the plp instances of the same equivalence class have the property that the aspect ratios of their items belong to an open interval of real numbers this interval characterises the plp equivalence classes and is referred to as the equivalence ratio interval eri by authors of this paper the time complexity of the new algorithm is two polynomial orders lower than that of the best known algorithm the authors of this paper also suggest that the concept of msi and its identifying algorithm can be used to transform the non integer plp into its equivalent integer msi

the hypertoric intersection cohomology ring we present a functorial computation of the equivariant intersection cohomology of a hypertoric variety and endow it with a natural ring structure when the hyperplane arrangement associated with the hypertoric variety is unimodular we show that this ring structure is induced by a ring structure on the equivariant intersection cohomology sheaf in the equivariant derived category the computation is given in terms of a localization functor which takes equivariant sheaves on a sufficiently nice stratified space to sheaves on a poset

an and or graph approach to the solution of two dimensional non guillotine cutting problems this work is concerned with unconstrained two dimensional non guillotine cutting problems where a rectangular plate is cut into a number of rectangular pieces in such a way as to optimize an objective function we reduce the state space of the problem by considering non guillotine cutting patterns which are combinations of guillotine and simple non guillotine cuts these cutting patterns are represented as complete paths in an and or graph and a branch and bound method is described we provide rules and heuristics that reduce the graph search and present computational results from randomly generated examples as well as from the literature

lifshitz tails for random schrodinger operators with negative singular poisson potential we develop a method of asymptotic study of the integrated density of states ids n e of a random schrodinger operator with a non positive attractive poisson potential the method is based on the periodic approximations of the potential instead of the dirichlet neumann bracketing used before this allows us to derive more precise bounds for the rate of approximations of the ids by the ids of respective periodic operators and to obtain rigorously for the first time the leading term of log n e as e for the poisson random potential with a singular single site impurity potential in particular for the screened coulomb impurities dislocations etc

gkm theory and hamiltonian non kahler actions in dimension 6 abstract using the classification of 6 dimensional manifolds by wall jupp and ubr we observe that the diffeomorphism type of simply connected compact 6 dimensional integer gkm t 2 manifolds is encoded in their gkm graph as an application we show that the 6 dimensional manifolds on which tolman and woodward constructed hamiltonian non kahler t 2 actions with finite fixed point set are diffeomorphic to eschenburg s twisted flag manifold su 3 t 2 in particular they admit a noninvariant kahler structure

configuration spaces and polyhedral products abstract this paper aims to find the most general combinatorial conditions under which a moment angle complex d 2 s 1 k is a co h space thus splitting unstably in terms of its full subcomplexes in this way we study to which extent the conjecture holds that a moment angle complex over a golod simplicial complex is a co h space our main tool is a certain generalisation of the theory of labelled configuration spaces

colorings of simplicial complexes and vector bundles over davis januszkiewicz spaces we show that coloring properties of a simplicial complex k are reflected by splitting properties of a bundle over the associated davis januszkiewicz space whose chern classes are given by the elementary symmetric polynomials in the generators of the stanley reisner algebra of k

torus graphs and simplicial posets for several important classes of manifolds acted on by the torus the information about the action can be encoded combinatorially by a regular n valent graph with vector labels on its edges which we refer to as the torus graph by analogy with the gkm graphs we introduce the notion of equivariant cohomology of a torus graph and show that it is isomorphic to the face ring of the associated simplicial poset this extends a series of previous results on the equivariant cohomology of torus manifolds as a primary combinatorial application we show that a simplicial poset is cohen macaulay if its face ring is cohen macaulay this completes the algebraic characterisation of cohen macaulay posets initiated by stanley we also study blow ups of torus graphs and manifolds from both the algebraic and the topological points of view

combinatorial stratification of complex arrangements we present a method for discretizing complex hyperplane arrange ments by encoding their topology into a finite partially ordered set of sign vectors this is used in the following ways 1 a general method is given for constructing regular cell complexes having the homotopy type of the complement of the arrangement 2 for the case of complexified arrangements this specializes to the con struction of salvetti s we study the combinatorial structure of complexified arrangements and the salvetti complex in some detail 3 this general method simultaneously produces cell decompositions of the singularity link this link is shown to have the homotopy type of a wedge of d spheres for arrangements in cd d 4 4 the homology of the link and the cohomology of the complement are computed in terms of explicit bases which are matched by alexander duality this gives a new more elementary and more generally valid proof for the brieskorn orlik solomon theorem and some related results 5 our setup leads to a more general notion of 2 pseudoarrangements which can be thought of as topologically deformed complex arrangements re taining only the essential topological and combinatorial structure we show that all of the above remains true in this generality except for the sign patterns of the orlik solomon relations department of mathematics royal institute of technology s10044 stockholm sweden e mail address andersb nada kth se institut fur mathematik universitat augsburg d 8900 augsburg germany current address institut mittag leffler auravagen 17 s 18262 djursholm sweden address after 1 april 1992 konrad zuse zentrum fur informationstechnik berlin heilbronner str 10 w 1000 berlin 31 germany e mail addresses ziegler ml kva se ziegler zib berlin de this content downloaded from 157 55 39 211 on fri 24 jun 2016 06 44 45 utc all use subject to http about jstor org terms