Download or read book Intersection Cohomology written by Armand Borel and published by Springer Science & Business Media. This book was released on 2009-05-21 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a publication in Swiss Seminars, a subseries of Progress in Mathematics. It is an expanded version of the notes from a seminar on intersection cohomology theory, which met at the University of Bern, Switzerland, in the spring of 1983. This volume supplies an introduction to the piecewise linear and sheaf-theoretic versions of that theory as developed by M. Goresky and R. MacPherson in Topology 19 (1980), and in Inventiones Mathematicae 72 (1983). Some familiarity with algebraic topology and sheaf theory is assumed.
Download or read book An Introduction to Intersection Homology Theory Second Edition written by Frances Kirwan and published by CRC Press. This book was released on 2006-06-07 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now more that a quarter of a century old, intersection homology theory has proven to be a powerful tool in the study of the topology of singular spaces, with deep links to many other areas of mathematics, including combinatorics, differential equations, group representations, and number theory. Like its predecessor, An Introduction to Intersection Homology Theory, Second Edition introduces the power and beauty of intersection homology, explaining the main ideas and omitting, or merely sketching, the difficult proofs. It treats both the basics of the subject and a wide range of applications, providing lucid overviews of highly technical areas that make the subject accessible and prepare readers for more advanced work in the area. This second edition contains entirely new chapters introducing the theory of Witt spaces, perverse sheaves, and the combinatorial intersection cohomology of fans. Intersection homology is a large and growing subject that touches on many aspects of topology, geometry, and algebra. With its clear explanations of the main ideas, this book builds the confidence needed to tackle more specialist, technical texts and provides a framework within which to place them.
Download or read book Intersection Homology Perverse Sheaves written by Laurenţiu G. Maxim and published by Springer Nature. This book was released on 2019-11-30 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout. By giving a taste of the main ideas in the field, the author welcomes new readers to this exciting area at the crossroads of topology, algebraic geometry, analysis, and differential equations. Those looking to delve further into the abstract theory will find ample references to facilitate navigation of both classic and recent literature. Beginning with an introduction to intersection homology from a geometric and topological viewpoint, the text goes on to develop the sheaf-theoretical perspective. Then algebraic geometry comes to the fore: a brief discussion of constructibility opens onto an in-depth exploration of perverse sheaves. Highlights from the following chapters include a detailed account of the proof of the Beilinson–Bernstein–Deligne–Gabber (BBDG) decomposition theorem, applications of perverse sheaves to hypersurface singularities, and a discussion of Hodge-theoretic aspects of intersection homology via Saito’s deep theory of mixed Hodge modules. An epilogue offers a succinct summary of the literature surrounding some recent applications. Intersection Homology & Perverse Sheaves is suitable for graduate students with a basic background in topology and algebraic geometry. By building context and familiarity with examples, the text offers an ideal starting point for those entering the field. This classroom-tested approach opens the door to further study and to current research.
Download or read book Intersection Cohomology Simplicial Blow Up and Rational Homotopy written by David Chataur and published by American Mathematical Soc.. This book was released on 2018-08-09 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let X be a pseudomanifold. In this text, the authors use a simplicial blow-up to define a cochain complex whose cohomology with coefficients in a field, is isomorphic to the intersection cohomology of X, introduced by M. Goresky and R. MacPherson. The authors do it simplicially in the setting of a filtered version of face sets, also called simplicial sets without degeneracies, in the sense of C. P. Rourke and B. J. Sanderson. They define perverse local systems over filtered face sets and intersection cohomology with coefficients in a perverse local system. In particular, as announced above when X is a pseudomanifold, the authors get a perverse local system of cochains quasi-isomorphic to the intersection cochains of Goresky and MacPherson, over a field. We show also that these two complexes of cochains are quasi-isomorphic to a filtered version of Sullivan's differential forms over the field Q. In a second step, they use these forms to extend Sullivan's presentation of rational homotopy type to intersection cohomology.
Download or read book An Introduction to Intersection Homology Theory written by Frances Clare Kirwan and published by Halsted Press. This book was released on 1988 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Singular Intersection Homology written by Greg Friedman and published by Cambridge University Press. This book was released on 2020-09-24 with total page 823 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first expository book-length introduction to intersection homology from the viewpoint of singular and piecewise linear chains.
Download or read book Singular Intersection Homology written by Greg Friedman and published by Cambridge University Press. This book was released on 2020-09-24 with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intersection homology is a version of homology theory that extends Poincaré duality and its applications to stratified spaces, such as singular varieties. This is the first comprehensive expository book-length introduction to intersection homology from the viewpoint of singular and piecewise-linear chains. Recent breakthroughs have made this approach viable by providing intersection homology and cohomology versions of all the standard tools in the homology tool box, making the subject readily accessible to graduate students and researchers in topology as well as researchers from other fields. This text includes both new research material and new proofs of previously-known results in intersection homology, as well as treatments of many classical topics in algebraic and manifold topology. Written in a detailed but expository style, this book is suitable as an introduction to intersection homology or as a thorough reference.
Download or read book Intersection Spaces Spatial Homology Truncation and String Theory written by Markus Banagl and published by Springer. This book was released on 2010-06-16 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intersection cohomology assigns groups which satisfy a generalized form of Poincaré duality over the rationals to a stratified singular space. This monograph introduces a method that assigns to certain classes of stratified spaces cell complexes, called intersection spaces, whose ordinary rational homology satisfies generalized Poincaré duality. The cornerstone of the method is a process of spatial homology truncation, whose functoriality properties are analyzed in detail. The material on truncation is autonomous and may be of independent interest tohomotopy theorists. The cohomology of intersection spaces is not isomorphic to intersection cohomology and possesses algebraic features such as perversity-internal cup-products and cohomology operations that are not generally available for intersection cohomology. A mirror-symmetric interpretation, as well as applications to string theory concerning massless D-branes arising in type IIB theory during a Calabi-Yau conifold transition, are discussed.
Download or read book Handbook of Geometry and Topology of Singularities II written by José Luis Cisneros-Molina and published by Springer Nature. This book was released on 2021-11-01 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of the Handbook of the Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of ten chapters which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory and related topics. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
Download or read book Topological Invariants of Stratified Spaces written by Markus Banagl and published by Springer Science & Business Media. This book was released on 2007-02-16 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this book is the restoration of Poincaré duality on stratified singular spaces by using Verdier-self-dual sheaves such as the prototypical intersection chain sheaf on a complex variety. Highlights include complete and detailed proofs of decomposition theorems for self-dual sheaves, explanation of methods for computing twisted characteristic classes and an introduction to the author's theory of non-Witt spaces and Lagrangian structures.
Download or read book Extending Intersection Homology Type Invariants to Non Witt Spaces written by Markus Banagl and published by American Mathematical Soc.. This book was released on 2002 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intersection homology theory provides a way to obtain generalized Poincare duality, as well as a signature and characteristic classes, for singular spaces. For this to work, one has had to assume however that the space satisfies the so-called Witt condition. We extend this approach to constructing invariants to spaces more general than Witt spaces.
Download or read book Geometric Invariant Theory written by David Mumford and published by Springer Science & Business Media. This book was released on 1994 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Geometric Invariant Theory" by Mumford/Fogarty (the firstedition was published in 1965, a second, enlarged editonappeared in 1982) is the standard reference on applicationsof invariant theory to the construction of moduli spaces.This third, revised edition has been long awaited for by themathematical community. It is now appearing in a completelyupdated and enlarged version with an additional chapter onthe moment map by Prof. Frances Kirwan (Oxford) and a fullyupdated bibliography of work in this area.The book deals firstly with actions of algebraic groups onalgebraic varieties, separating orbits by invariants andconstructionquotient spaces; and secondly with applicationsof this theory to the construction of moduli spaces.It is a systematic exposition of the geometric aspects ofthe classical theory of polynomial invariants.
Download or read book Stratified Morse Theory written by Mark Goresky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to the lack of proper bibliographical sources stratification theory seems to be a "mysterious" subject in contemporary mathematics. This book contains a complete and elementary survey - including an extended bibliography - on stratification theory, including its historical development. Some further important topics in the book are: Morse theory, singularities, transversality theory, complex analytic varieties, Lefschetz theorems, connectivity theorems, intersection homology, complements of affine subspaces and combinatorics. The book is designed for all interested students or professionals in this area.
Download or read book The Intersection Homology D module in Finite Characteristic written by Manuel Blickle and published by . This book was released on 2001 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Analysis And Geometry In Foliated Manifolds Proceedings Of The 7th International Colloquium On Differential Geometry written by Enrique Macias-virgos and published by World Scientific. This book was released on 1995-11-17 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this volume, recent developments in foliation theory and important related analytic and geometric techniques, is an active field in the application of both global analysis and geometric topological theory of manifolds to the study of foliations. This volume includes research papers by leading specialists, giving an overview of this subject.
Download or read book Topology of Stratified Spaces written by Greg Friedman and published by Cambridge University Press. This book was released on 2011-03-28 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the study of singular spaces using techniques from areas within geometry and topology and the interactions among them.
