Singular Intersection Homology PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Singular Intersection Homology PDF full book. Access full book title Singular Intersection Homology.
Author | : Greg Friedman |
Publisher | : Cambridge University Press |
Total Pages | : 823 |
Release | : 2020-09-24 |
Genre | : Mathematics |
ISBN | : 1107150744 |
Download Singular Intersection Homology Book in PDF, ePub and Kindle
The first expository book-length introduction to intersection homology from the viewpoint of singular and piecewise linear chains.
Author | : Laurenţiu G. Maxim |
Publisher | : Springer Nature |
Total Pages | : 270 |
Release | : 2019-11-30 |
Genre | : Mathematics |
ISBN | : 3030276449 |
Download Intersection Homology & Perverse Sheaves Book in PDF, ePub and Kindle
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.
Author | : Armand Borel |
Publisher | : Springer Science & Business Media |
Total Pages | : 243 |
Release | : 2009-05-21 |
Genre | : Mathematics |
ISBN | : 0817647651 |
Download Intersection Cohomology Book in PDF, ePub and Kindle
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.
Author | : Frances Clare Kirwan |
Publisher | : Halsted Press |
Total Pages | : 169 |
Release | : 1988 |
Genre | : Algebra, Homological |
ISBN | : 9780470211984 |
Download An Introduction to Intersection Homology Theory Book in PDF, ePub and Kindle
Author | : Frances Kirwan |
Publisher | : CRC Press |
Total Pages | : 250 |
Release | : 2006-06-07 |
Genre | : Mathematics |
ISBN | : 9781584881841 |
Download An Introduction to Intersection Homology Theory, Second Edition Book in PDF, ePub and Kindle
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.
Author | : Markus Banagl |
Publisher | : American Mathematical Soc. |
Total Pages | : 101 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 0821829882 |
Download Extending Intersection Homology Type Invariants to Non-Witt Spaces Book in PDF, ePub and Kindle
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.
Author | : Mark Goresky |
Publisher | : Springer Science & Business Media |
Total Pages | : 279 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642717144 |
Download Stratified Morse Theory Book in PDF, ePub and Kindle
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.
Author | : Markus Banagl |
Publisher | : Springer Science & Business Media |
Total Pages | : 266 |
Release | : 2007-02-16 |
Genre | : Mathematics |
ISBN | : 3540385878 |
Download Topological Invariants of Stratified Spaces Book in PDF, ePub and Kindle
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.
Author | : Jörg Schürmann |
Publisher | : Birkhäuser |
Total Pages | : 461 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034880618 |
Download Topology of Singular Spaces and Constructible Sheaves Book in PDF, ePub and Kindle
This volume is based on the lecture notes of six courses delivered at a Cimpa Summer School in Temuco, Chile, in January 2001. Leading experts contribute with introductory articles covering a broad area in probability and its applications, such as mathematical physics and mathematics of finance. Written at graduate level, the lectures touch the latest advances on each subject, ranging from classical probability theory to modern developments. Thus the book will appeal to students, teachers and researchers working in probability theory or related fields.
Author | : Markus Banagl |
Publisher | : Springer |
Total Pages | : 237 |
Release | : 2010-06-16 |
Genre | : Mathematics |
ISBN | : 3642125891 |
Download Intersection Spaces, Spatial Homology Truncation, and String Theory Book in PDF, ePub and Kindle
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.