some applications of gabai s internal hierarchy any haken 3 manifold possibly with boundary consisting of tori can be transformed into a surface s 1 by a series of splitting and regluing along incompressible surfaces this fact was proved by gabai as an application of his sutured manifold theory the first half of this paper provides a few technical details in the proof in the second half of this paper some applications of gabai s theorem to heegaard floer homology are given we refine the known results about the thurson norm and fibrations we also give some classification results for floer simple knots in manifolds with positive b 1

knots sutures and excision we develop monopole and instanton floer homology groups for balanced sutured manifolds in the spirit of 12 applications include a new proof of property p for knots

tilting modules and tilting torsion theories abstract we generalize basic results about classical tilting modules and partial tilting modules to the infinite dimensional case over an arbitrary ring r the methods employed combine classical techniques of representation theory of finite dimensional algebras with new techniques of the theory of modules using a generalization of the bongartz lemma we characterize tilting torsion theories in mod r i e torsion theories induced by infinitely generated tilting modules we investigate lattices gen p p of torsion classes induced by partial tilting modules p applying our results to tilting torsion classes we prove a version of the brenner butler theorem and a generalization of the assem smalo theorem to the case when r is artinian

an algorithm for computing some heegaard floer homologies in this paper we give an algorithm to compute the hat version of heegaard floer homology of a closed oriented three manifold this method also allows us to compute the filtration coming from a null homologous link in a three manifold

optimal rates of convergence for estimates of the extreme value index hall and welsh established the best attainable rate of convergence for estimates of a positive extreme value index y under a certain second order condition implying that the distribution function of the maximum of n random variables converges at an algebraic rate to the pertaining extreme value distribution as a first generalization we obtain a surprisingly sharp bound on the estimation error if y is still assumed to be positive but the rate of convergence of the maximum may be nonalgebraic this result allows a more accurate evaluation of the asymptotic performance of an estimator for y than the hall and welsh theorem for example it is proved that the hill and the pickands estimators achieve the optimal rate but only the hill estimator attains the sharp bound finally an analogous result is derived for a general not necessarily positive extreme value index in this situation it turns out that location invariant estimators show the best performance 1 introduction consider n i i d random variables r v s whose distribution function d f f belongs to the weak domain of attraction of an extreme value d f

kernel type estimators for the extreme value index a large part of the theory of extreme value index estimation is developed for positive extreme value indices the best known estimator of a positive extreme value index is probably the hill estimator this estimator belongs to the category of moment estimators but can also be interpreted as a quasi maximum likelihood estimator it has been generalized to a kernel type estimator but this kernel type estimator can similarly to the hill estimator only be used for the estimation of positive extreme value indices in the present paper we introduce kernel type estimators which can be used for estimating the extreme value index over the whole positive and negative range we present a number of results on their distributional behavior and compare their performance with the performance of other estimators such as moment type estimators for the whole range and the quasi maximum likelihood estimator based on the generalized pareto distribution we also discuss an automatic bandwidth selection method and introduce a kernel estimator for a second order parameter controlling the speed of convergence

holomorphic disks and topological invariants for closed three manifolds the aim of this article is to introduce certain topological invariants for closed oriented three manifolds y equipped with a spiny structure given a heegaard splitting of y u 0o u u 1 these theories are variants of the lagrangian floer homology for the g fold symmetric product of relative to certain totally real subspaces associated to u 0 and u 1

tilting classes over wild hereditary algebras in this paper we investigate tilting classes over connected hereditary algebras of in nite representation type and in particular over connected wild hereditary algebras thecase when the generating tilting module is nitely generated was studied in 13 in 17 lukas proved several facts important for our general setting in the present terminology heshowed that given a wild hereditary algebra

refined pickands estimators of the extreme value index consider a distribution function that belongs to the weak domain of attraction of an extreme value distribution the extreme value index will be estimated by mixtures of pickands estimators where the weights are generated by a probability measure which satisfies a certain integrability condition we prove a functional limit theorem for a process of pickands estimators and asymptotic normality of the refined pickands estimator for negative the new estimator is asymptotically superior to previously defined estimators a simulation study also demonstrates the good small sample performance in particular the estimator proves to be robust against an inappropriate choice of the number of upper order statistics used for estimation

exceptional components of wild hereditary algebras this paper studies regular components of wild hereditary algebras it is clear that the existence of extremely many maps in the infinite radical of the module category causes algebras to be wild whereas the dimension of the horn spaces of maps from indecomposable preprojective modules or to indecomposable preinjective modules can be calculated by linear methods via the euler bilinearform these methods give only poor information if we pass to regular modules so it is natural to study as a first step maps between regular modules which are in the same regular component v and we see in 4 7 that this is a way to get information about the maps between arbitrary regular modules there is another less obvious reason for the study of single components if a and b are connected wild hereditary algebras then by 9 via tilting modules there can be constructed bijections between the regular components of the auslander reiten quivers t a and t b in order to find finally properties of these bijections we have to study properties of components proposition 6 3 points in that direction if g is a regular component in t a with a wild hereditary we denote by the quasi rank rk of v the smallest integer n such that rad x r x 0 for all n 2 n and all xe we call a component v exceptional if there is an indecomposable quasi simple module xe such that hom x yx 0 but hom x z r 1 0 for some r 0 in section 4 we show that there are only finitely many exceptional components in t a and that the existence of those components has strict consequences for the algebra a that is for its ordinary quiver 9 a in section 5 we present the numerical invariants of the most important exceptional components in the last section we give applications to tilting theory the applications are chosen under the aspect that the notion of the quasi rank of a regular component might be a pendant to the period of a tube in the tame case 184 0021 8693 92 5 00

tilting for regular rings of krull dimension two we classify tilting classes over regular rings r of krull dimension two they are parametrized by the set of all pairs x y such that assrr x spec r y consists of maximal ideals of height 2 and y contains all the maximal ideals of height 2 that contain some element of x assrr for r local we also classify the corresponding infinitely generated tilting modules

heegaard floer homology of broken fibrations over the circle abstract we extend perutz s lagrangian matching invariants to 3 manifolds which are not necessarily fibered using the technology of holomorphic quilts we prove an isomorphism of these invariants with ozsvath szabo s heegaard floer invariants for certain extremal spin c structures as applications we give new calculations of heegaard floer homology of certain classes of 3 manifolds and a characterization of juhasz s sutured floer homology

holomorphic triangles and invariants for smooth four manifolds abstract in earlier articles the authors introduced invariants for closed oriented three manifolds defined using a variant of lagrangian floer homology in the symmetric products of riemann surfaces the aim of this article is to introduce invariants of oriented smooth four manifolds built using these floer homology groups this four dimensional theory also endows the corresponding three dimensional theories with additional structure an absolute grading of certain of its floer homology groups

holomorphic disks and three manifold invariants properties and applications in 27 we introduced floer homology theories hf y s hf y s hf y t hf y s and hf red y s associated to closed oriented three manifolds y equipped with a spiny structures s spin c y in the present paper we give calculations and study the properties of these invariants the calculations suggest a conjectured relationship with seiberg witten theory the properties include a relationship between the euler characteristics of hf and turaev s torsion a relationship with the minimal genus problem thurston norm and surgery exact sequences we also include some applications of these techniques to three manifold topology

geometric composition in quilted floer theory abstract we prove that floer cohomology of cyclic lagrangian correspondences is invariant under transverse and embedded composition under a general set of assumptions

whitehead test modules a right r module n is said to be a whitehead test module for projectivity shortly a p test module provided for each module m extr m n 0 implies m is projective dually i test modules are defined for example z is a p test abelian group iff each whitehead group is free our first main result says that if r is a right hereditary non right perfect ring then the existence of p test modules is independent of zfc gch on the other hand for any ring r there is a proper class of i test modules dually there is a proper class of p test modules over any right perfect ring a non semisimple ring r is said to be fully saturated saturated provided that all non projective generated non projective modules are i test we show that classification of saturated rings can be reduced to the indecomposable ones indecomposable 1 saturated rings fall into two classes type i where all simple modules are isomorphic and type ii the others our second main result gives a complete characterization of rings of type ii as certain generalized upper triangular matrix rings gt 1 n p s t the four parameters involved here are skew fields s and t and natural numbers n p for rings of type i we have several partial results e g using a generalization of bongartz lemma we show that it is consistent that each fully saturated ring of type i is a full matrix ring over a local quasi frobenius ring in several recent papers our results have been applied to tilting theory and to the theory of modules in modern algebra the structure of rings r is studied by means of properties of corresponding module categories mod r in most cases it is not possible to characterize mod r fully nevertheless there are important subclasses of mod r that can be treated in detail and that shed light on the whole of mod r among the prominent ones are the classes of all projective and all injective modules recall that a module m is said to be projective injective provided that the functorhomr m homr m preserves short exact sequences there is also a universal algebraic aspect each module is a factor module of a projective module and a submodule of an injective module so a possible strategy to investigate modr consists in describing all injective modules and for each injective module i all its submodules the first step is usually relatively easy but the second may be quite hard for example using this strategy for abelian groups one meets serious difficulties already for i q q see e g e theorem 2 received by the editors march 17 1995 1991 mathematics subject classification primary 16e30 secondary 03e35 20k35