Topology of Singular Spaces and Constructible Sheaves

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.

A new cohomological approach to constructible sheaves on stratified spaces, which doesn't use the first isotopy lemma of Thom A self-contained approach to Morse theory for constructible sheaves, including a geometric introduction to the theory of characteristic cycles Very general vanishing and Lefschetz theorems of Artin-Grothendieck type in the complex algebraic and analytic context, which apply in particular to intersection (co)homology and perverse sheaves

Contenu
1 Thom-Sebastiani Theorem for constructible sheaves.- 1.1 Milnor fibration.- 1.2 Thom-Sebastiani Theorem.- 1.3 The Thom-Sebastiani Isomorphism in the derived category.- 1.4 Appendix: Künneth formula.- 2 Constructible sheaves in geometric categories.- 2.1 Geometric categories.- 2.2 Constructible sheaves.- 2.3 Constructible functions.- 3 Localization results for equivariant constructible sheaves.- 3.1 Equivariant sheaves.- 3.2 Localization results for additive functions.- 3.3 Localization results for Grothendieck groups and trace formulae.- 3.4 Equivariant cohomology.- 4 Stratification theory and constructible sheaves.- 4.1 Stratification theory.- 4.2 Constructible sheaves on stratified spaces.- 4.3 Base change properties.- 5 Morse theory for constructible sheaves.- 5.1 Stratified Morse theory, part I.- 5.2 Characteristic cycles and index formulae.- 5.3 Stratified Morse theory, part II.- 5.4 Vanishing cycles.- 6 Vanishing theorems for constructible sheaves.- Introduction: Results and examples.- 6.1 Proof of the results.