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基本説明
Features a chapter on intersection homology toric varieties and the link with the theory of convex polytopes.
Full 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.
Contents
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.
