Topology of Stratified Spaces

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

• ISBN13: 9780521191678
• ISBN10: 052119167X
• Format: Hardcover
• Copyright: 2011-03-28
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

Preface	p. ix
An introduction to L2 cohomology	p. 1
The almost closed range condition	p. 13
Rigidity of differential operators and Chern numbers of singular varieties	p. 31
Hodge theory meets the minimal model program: a survey of log canonical and du Bois singularities	p. 51
Elliptic genera, real algebraic varieties and quasi-Jacobi forms	p. 95
The weight filtration for real algebraic varieties	p. 121
On the Milnor classes of complex hypersurfaces	p. 161
An introduction to intersection homology with general perversity functions	p. 177
The signature of singular spaces and its refinements to generalized homology theories	p. 223
Intersection homology Wang sequence	p. 251
An exponential history of functions with logarithmic growth	p. 281
Motivic characteristic classes	p. 375
Characteristic classes of mixed Hodge modules	p. 419
Open problems	p. 471
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