
An Introduction to Intersection Homology Theory
Chapman & Hall/CRC (Publisher)
2nd Edition
Published on 7. June 2006
Book
Hardback
246 pages
978-1-58488-184-1 (ISBN)
Description
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.
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.
More details
Edition
2nd edition
Language
English
Place of publication
Oxford
United States
Publishing group
Taylor & Francis Inc
Target group
College/higher education
Professional and scholarly
Undergraduate
Illustrations
10 s/w Abbildungen
10 Illustrations, black and white
Dimensions
Height: 234 mm
Width: 156 mm
Weight
476 gr
ISBN-13
978-1-58488-184-1 (9781584881841)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
Frances Kirwan, Jonathan Woolf
Author
Balliol College, University of Oxford, UK
University of Liverpool, UK
Content
Introduction. Review of Homology and Cohomology. Review of Sheaf Cohomology and Derived Categories. The Definition of Intersection Homology. Witt Spaces and Duality. L2-Cohomology and Intersection Cohomology. Sheaf-Theoretic Intersection Homology. Perverse Sheaves. The Intersection Cohomology of Fans. Characteristic p and the Weil Conjectures. D-Modules and the Riemann-Hilbert Correspondence. The Kazhdan-Lusztig Conjecture. Bibliography. Index.