Topology of Stratified Spaces

1. Auflage 2011
ISBN: 978-0-521-19167-8
Verlag: Cambridge University Press

Buch, Englisch, 488 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 895 g

Reihe: Mathematical Sciences Research Institute Publications

• Provides expository papers on the topology of stratified spaces as opposed to new research
• Provides an interdisciplinary discussion within the world of stratified space research
• Offers special introductory papers written by experts from the field

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.

Autoren/Hrsg.

Friedman, Greg

Hunsicker, Eugenie

Libgober, Anatoly

Maxim, Laurentiu

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie

Inhaltsverzeichnis

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