An Introduction to Intersection Homology Theory, Second EditionCRC Press, 7 juin 2006 - 248 pages 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. |
Table des matières
Introduction | 1 |
Review of homology and cohomology | 15 |
Review of sheaf cohomology and derived categories | 25 |
The definition of intersection homology | 49 |
Witt spaces and duality | 73 |
L2cohomology and intersection cohomology | 85 |
Sheaftheoretic intersection homology | 103 |
Perverse sheaves | 117 |
The intersection cohomology of fans | 133 |
Characteristic p and the Weil conjectures | 163 |
The KazhdanLusztig conjecture | 199 |
| 211 | |
| 225 | |
Expressions et termes fréquents
Abelian algebraic Beilinson Bernstein Borel Ch(M Chapter codimension coefficients cohomology compact complex of sheaves complex projective variety compute cone conjecture constant sheaf convex decomposition defined Definition derived category differential system dimension dual equivalence equivariant étale Example fibre finite follows function functor generalised Goresky and MacPherson H²(X Hodge holomorphic homeomorphism homology groups Homsh(x hypercohomology hyperplane i-chain IH(X induces injective resolution intersection homology intersection homology groups irreducible isomorphism Kashiwara l-adic L2-cohomology linear locally symmetric MacPherson 70 manifold map f metric middle perversity module natural map non-singular open subset perverse sheaves Poincaré duality polynomial polytope presheaf projective variety proof Proposition quasi-isomorphism quasi-projective variety quotient rational fan restriction maps Rham Riemann-Hilbert correspondence satisfies simplicial stalk stratification stratum subspace subvariety Suppose surjective Theorem theory topological pseudomanifold topological space toric variety torus triangulation unique vector space Verdier duality Witt space
Fréquemment cités
Page 212 - A. Beilinson, V. Ginzburg, and W. Soergel, Koszul duality patterns in representation theory.
Page 213 - Transformations canoniques, dualite projective, theorie de Lefschetz, transformations de Fourier et sommes trigonometriques.
Page 224 - GM Ziegler. Lectures on Polytopes, volume 152 of Graduate Texts in Mathematics. Springer- Verlag, New York, 1995.
Page 212 - A. Borel and JC Moore. Homology theory for locally compact spaces, Mich. Math.
Page 213 - Braden and R. MacPherson. Intersection homology of toric varieties and a conjecture of Kalai. Comment. Math. Helv., 74(3):442-455, 1999.