existence of simply connected algebraic surfaces of general type with positive and zero indices abstract in the classification problem of algebraic surfaces of general type an important conjecture states that for simply connected such surfaces chern numbers satisfy the inequality c12 2c2 or equivalently the index 0 we disprove this conjecture by computing fundamental groups of galois coverings corresponding to generic cp2 projections of projective embeddings of cp1 cp1 related to linear systems unk al1 bl2 unk a 3 b 2 also we proved the existence of simply connected minimal surfaces of general type with zero index e g c12 2c2 previously it was conjectured that these are exactly the surfaces uniformizable in the polydisk so this conjecture is also disproved

simplifying stable mappings into the plane from a global viewpoint let f m r2 be a c stable map of an n dimensional manifold into the plane the main purpose of this paper is to define a global surgery operation on f which simplifies the configuration of the critical value set and which does not change the diffeomorphism type of the source manifold m for this purpose we also study the quotient space wf of f which is the space of the connected components of the fibers of f and we completely determine its local structure for arbitrary dimension n of the source manifold m this is a completion of the result of kushner levine and porto for dimension 3 and that of furuya for orientable manifolds of dimension 4 we also pay special attention to dimension 4 and obtain a simplification theorem for stable maps whose regular fiber is a torus or a 2 sphere which is a refinement of a result of kobayashi

floer homology groups for homology three spheres recently floer fl has defined eight new homology groups for oriented 3 dimensional homology spheres the definition of these groups makes heavy use of the theory of gauge fields on threeand four manifolds as it has been developed during the last decade by uhlenbeck taubes donaldson and others the purpose of this note is to give an introductory rather detailed description of these interesting groups we also discuss some further structure on these groups the computations of floer homology for the brieskorn homology 3 spheres by fintushel and stern and the relation with donaldson polynomials for 4 manifolds here and there some further conjectures have been inserted apart from a few remarks in 94 nothing in these notes is due to the author and the credit for this work should go to floer the designers of gauge theory mentioned above and fintushel and stern very interestingly witten w2 has recently given a quantum field theory approach to floer homology and donaldson polynomials this we shall not review here also we shall not enter into a discussion on how to relate floer homology to two dimensional gauge theory through a heegaard splitting of the homology sphere this last point as well as much other beautiful scenery around floer s theory can be found in atiyah at

right bregman nonexpansive operators in banach spaces abstract we introduce and study new classes of bregman nonexpansive operators in reflexive banach spaces these classes of operators are associated with the bregman distance induced by a convex function in particular we characterize sunny right quasi bregman nonexpansive retractions and as a consequence we show that the fixed point set of any right quasi bregman nonexpansive operator is a sunny right quasi bregman nonexpansive retract of the ambient banach space

the geography problem for irreducible spin four manifolds we study the geography problem for smooth irreducible simplyconnected spin four manifolds for a large class of hoinotopy types we exhibit both symplectic and non symplectic representatives we also compute the seiberg witten invariants of all the four manifolds we construct

on the diffeomorphism types of certain algebraic surfaces i l invariant de donaldson la geometrie de certaines surfaces rationnelles surfaces dolgachev generalites sur des formes de type 1 n la classe canonique d une chambre et un coin le cone de kahler d une bonne surface generique une etude de p cellules les super p cellules

on the behavior of some estimators from probability plots abstract probability plots are popular graphical methods used to assess distributional assumptions under a location scale model the plot tends to lie on a straight line a common practice in this situation is to fit a line through the plot and use the intercept and slope of the fitted line as estimates of the location and scale parameters what are the properties of these estimators estimators from weighted least squares lines are considered and their asymptotic finite sample robustness and optimality properties are discussed included among these are the ordinary least squares estimators and estimators from least squares lines fitted after trimming or winsorizing some of the extreme order statistics

computations of instanton invariants using donaldson floer theory we compute the donaldson su 2 invariants of the double cover of 2 branched over a smooth algebraic curve of degree eight from this we deduce a formula for the relative invariants of the blow up of the gompf nucleusn2 and we show how this gives a blow up formula for a class of 4 manifolds which includes essentially all the simply connected 4 manifolds known to have big diffeomorphism group we apply the result on the nucleus also to prove a formula for the invariants of minimal simply connected elliptic surfaces which reduces the computation to the case of geometric genus one in particular we compute all the donaldson invariants of minimal simply connected elliptic surfaces without multiple fibers our main tool is donaldson floer theory

the geography of spin symplectic 4 manifolds in this paper we construct a family of simply connected spin non complex symplectic 4 manifolds which cover all but finitely many allowed lattice points chi mathbf c lying in the region 0 leq mathbf c leq 8 76 chi furthermore as a corollary we prove that there exist infinitely many exotic smooth structures on 2n 1 s 2 times s 2 for all n large enough

bregman strongly nonexpansive operators in reflexive banach spaces abstract we present a detailed study of right and left bregman strongly nonexpansive operators in reflexive banach spaces we analyze in particular compositions and convex combinations of such operators and prove the convergence of the picard iterative method for operators of these types finally we use our results to approximate common zeros of maximal monotone mappings and solutions to convex feasibility problems

an algorithm for finding a common point of the solution set of a variational inequality and the fixed point set of a bregman relatively nonexpansive mapping in this paper we investigate an iterative scheme for finding a common point of the solution set of a variational inequality and the fixed point set of a bregman relatively nonexpansive mapping moreover a numerical example which shows the conclusion of our result is presented our results improve and generalize many known results in the current literature

an instanton invariant for 3 manifolds to an oriented closed 3 dimensional manifoldm withh1 m 0 we assign a 8 graded homology groupi m whose euler characteristic is twice casson s invariant the definition uses a construction on the space of instantons onm

iterating bregman retractions the notion of a bregman retraction of a closed convex set in euclidean space is introduced bregman retractions include backward bregman projections and forward bregman projections as well as their convex combinations and are thus quite flexible the main result on iterating bregman retractions unifies several convergence results on projection methods for solving convex feasibility problems it is also used to construct new sequential and parallel algorithms

the orientation of yang mills moduli spaces and 4 manifold topology si x est une 4 variete lisse orientee fermee dont la forme intersection q h 2 x z torsion z est definie negative alors la forme est equivalente sur les entiers a la forme standard 1 1 1 soit x une 4 variete lisse orientee fermee avec les trois proprietes suivantes 1 h 1 x z n a pas de 2 torsion 2 la forme intersection q sur h 2 x torsion a une partie positive de rang 1 ou 2 3 la forme intersection est paire alors q est equivalente sur les entiers a une des formes 01 10 01 10 01 10

instanton homology of seifert fibred homology three spheres for an oriented integral homology 3 sphere 2 a casson has introduced an integer invariant a 2 that is defined by using the space 2 of conjugacy classes of irreducible representations of 2 into su 2 see 1 this invariant a 2 can be computed from a surgery or heegard description of 2 and satisfies a 2 ju 2 mod 2 where i 2 is the kervaire milnor rochlin invariant of 2 this powerful new invariant was used to settle an outstanding problem in 3 manifold topology namely showing that if 2 is a homotopy 3 sphere then ju 2 o c taubes 17 utilizing gauge theoretic considerations has reinterpreted casson s invariant in terms of flat connections refining this approach a floer 13 has recently defined another invariant of 2 its instanton homology which takes the form of an abelian group 2 with a natural z8 grading that is an enhancement of a 2 in that

representations of knot groups in su 2 this paper is a study of the structure of the space r k of representations of classical knot groups into su 2 let r k equal the set of conjugacy classes of irreducible representations in gi we interpret the relations in a presentation of the knot group in terms of the geometry of su 2 using this technique we calculate r k for k equal to the torus knots twist knots and the whitehead link we also determine a formula for the number of binary dihedral representations of an arbitrary knot group we prove using techniques introduced by culler and shalen that if the dimension of r k is greater than 1 then the complement in sj of a tubular neighborhood of k contains closed nonboundary parallel incompressible surfaces we also show how for certain nonprime and doubled knots r k has dimension greater than one in gii we calculate the zariski tangent space tp r k for an arbitrary knot k at a reducible representation p using a technique due to weil we prove that for all but a finite number of the reducible representations dimtp r k 3 these nonexceptional representations possess neighborhoods in r k containing only reducible representations at the exceptional representations which correspond to real roots of the alexander polynomial dim tp r k 3 2k for a positive integer k in those examples analyzed in this paper these exceptional representations can be expressed as limits of arcs of irreducible representations we also give an interpretation of these extra tangent vectors as representations in the group of euclidean isometries of the plane 0 introduction this paper is a study of the space r k of representations of the fundamental group of the complement of a knot k into the lie group su 2 the major results are as follows 1 a calculation of the topological type of r k for k a torus knot a twist knot or the whitehead link 2 a determination of the zariski tangent space to r k at a reducible representation for an arbitrary knot k and 3 a proposition and some examples relating the dimension of r k to incompressible surfaces in the complement of k while the idea of representing 3 manifold groups in su 2 is a fairly recent one the representation of these groups in other groups has a substantial history we will not attempt to chronicle this history in detail but will comment here on received by the editors january 18 1989 and in revised form july 25 1989 1980 mathematics subject classification 1985 revision primary 57m05 57m25

robust estimators of the generalized log gamma distribution we propose robust estimators of the generalized log gamma distribution and more generally of location shape scale families of distributions a weighted q estimator minimizes a scale of the differences between empirical and theoretical quantiles it is n1 2 consistent unfortunately it is not asymptotically normal and therefore inconvenient for inference however it is a convenient starting point for a one step weighted likelihood estimator where the weights are based on a disparity measure between the model density and a kernel density estimate the one step weighted likelihood estimator is asymptotically normal and fully efficient under the model it is also highly robust under outlier contamination supplementary materials are available online

bregman monotone optimization algorithms a broad class of optimization algorithms based on bregman distances in banach spaces is unified around the notion of bregman monotonicity a systematic investigation of this notion leads to a simplified analysis of numerous algorithms and to the development of a new class of parallel block iterative surrogate bregman projection schemes another key contribution is the introduction of a class of operators that is shown to be intrinsically tied to the notion of bregman monotonicity and to include the operators commonly found in bregman optimization methods special emphasis is placed on the viability of the algorithms and the importance of legendre functions in this regard various applications are discussed

topologically invariant chern numbers of projective varieties abstract we prove that a rational linear combination of chern numbers is an oriented diffeomorphism invariant of smooth complex projective varieties if and only if it is a linear combination of the euler and pontryagin numbers in dimension at least three we prove that only multiples of the top chern number which is the euler characteristic are invariant under diffeomorphisms that are not necessarily orientation preserving these results solve a long standing problem of hirzebruch s we also determine the linear combinations of chern numbers that can be bounded in terms of betti numbers

iterative methods for solving systems of variational inequalities in reflexive banach spaces we prove strong convergence theorems for three iterative algorithms which approximate solutions to systems of variational inequalities for mappings of monotone type all the theorems are set in reflexive banach spaces and take into account possible computational errors

connections with l p bounds on curvature we show by means of the implicit function theorem that coulomb gauges exist for fields over a ball inr n when the integrall n 2 field norm is sufficiently small we then are able to prove a weak compactness theorem for fields on compact manifolds withl p integral norms bounded p n 2

surgery in cusp neighborhoods and the geography of irreducible 4 manifolds since its inception the theory of smooth 4 manifolds has relied upon complex surface theory to provide its basic examples this is especially true for simply connected 4 manifolds a longstanding conjecture held that every smooth simply connected closed 4 manifold is the connected sum of manifolds each admitting a complex structure with one of its orientations for this conjecture the 4 sphere was considered as the empty connected sum quite recently this was disproved by gompf and mrowka gm1 who produced infinite families of examples of 4 manifolds homeomorphic to the k3 surface and which admit no complex structure with either orientation the discovery of these dramatic counterexamples to the h cobordism theorem in dimension 4 was the most recent success in a long line of applications of donaldson invariants to the study of smooth structures on 4 manifolds beginning with donaldson s d4 and followed by fm1 ko ov1 ov2 which depended on donaldson s f invariant or a suitable generalization and fmm dk e2 eo1 mn2 sa using donaldson s polynomial invariant a common thread running through many of these counterexamples to the h cobordism conjecture is the process of logarithmic transformation which introduces multiple fibres in an elliptic surface in controlled situations this process will change the diffeomorphism type of a given elliptic surface while keeping its homotopy type fixed taking advantage of the complex structure on an elliptic surface this change can often be detected by using the relationship between anti self dual connections over a complex surface and stable holomorphic bundles d2 an alternative and more differential geometric

anti self dual yang mills connections over complex algebraic surfaces and stable vector bundles on presente une correspondance entre la geometrie algebrique et la geometrie differentielle des fibres vectoriels soit une surface algebrique projective x qui a un plongement donne x cp n et soit une metrique de kahler sur x dont la classe de cohomologie associee est duale a la classe de section d hyperplan h un fibre sur x est stable par rapport au plongement projectif si et seulement si il admet une connexion irreductible d hermite einstein par rapport a la metrique cette connexion est alors unique

on the rate of convergence of iterated bregman projections and of the alternating algorithm abstract we study the alternating algorithm for the computation of the metric projection onto the closed sum of two closed subspaces in uniformly convex and uniformly smooth banach spaces for banach spaces which are convex and smooth of power type we exhibit a condition which implies linear convergence of this method we show these convergence results for iterates of bregman projections onto closed linear subspaces using an intimate connection between the metric projection onto a closed linear subspace and the bregman projection onto its annihilator we deduce the convergence rate results for the alternating algorithm from the corresponding results for the iterated bregman projection method