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.
Reihe
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Maße
Höhe: 240 mm
Breite: 161 mm
Dicke: 31 mm
Gewicht
ISBN-13
978-0-521-19167-8 (9780521191678)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Herausgeber*in
Texas Christian University
Loughborough University
University of Illinois, Chicago
University of Wisconsin, Madison
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 Sandor J. Kovacs 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 Joerg Schuermann.
