Topology of Stratified Spaces

This book explores the study of singular spaces using techniques from areas within geometry and topology and the interactions among them.

Greg Friedman (Edited by), Eugénie Hunsicker (Edited by), Anatoly Libgober (Edited by), Laurentiu Maxim (Edited by)

9780521191678, Cambridge University Press

Hardback, published 28 March 2011

490 pages
23.4 x 15.6 x 2.7 cm, 0.86 kg

Appearance of singularities is pervasive in many problems in topology, differential geometry and algebraic geometry. This book concerns the study of singular spaces using techniques from a variety of areas of geometry and topology and the interactions among them. Expository chapters by well-known experts cover intersection homology, L2 cohomology and differential operators, topology of algebraic varieties, signatures and characteristic classes, mixed Hodge theory and elliptic genera of singular complex and real algebraic varieties. The book concludes with a list of open problems.

1. An introduction to L2 cohomology Xianzhe Dai
2. The almost closed range condition Gilles Carron
3. Rigidity of differential operators and Chern numbers of singular varieties Robert Waelder
4. Hodge theory meets the minimal model program: a survey of log canonical and du Bois singularities Sándor J. Kovács and Karl Schwede
5. Elliptic genera, real algebraic varieties and quasi-Jacobi forms Anatoly Libgober
6. The weight filtration for real algebraic varieties Clint McCrory and Adam Parusinski
7. On the Milnor classes of complex hypersurfaces Laurentiu Maxim
8. An introduction to intersection homology with general perversity functions Greg Friedman
9. The signature of singular spaces and its refinements to generalized homology theories Markus Banagl
10. Intersection homology Wang sequence Filipp Levikov
11. An exponential history of functions with logarithmic growth Matt Kerr and Gregory Pearlstein
12. Motivic characteristic classes Shoji Yokura
13. Characteristic classes of mixed Hodge modules Jörg Schürmann.

Subject Areas: Algebraic topology [PBPD], Topology [PBP], Geometry [PBM], Algebra [PBF]