Topology of Stratified Spaces [Paperback]

This book explores the study of singular spaces using techniques from areas within geometry and topology and the interactions among them.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.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.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 S?ndor J. Kov?cs 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 tl³2