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Topological Invariants of Stratified Spaces Markus Banagl

Topological Invariants of Stratified Spaces By Markus Banagl

Topological Invariants of Stratified Spaces by Markus Banagl


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Summary

The central theme of this book is the restoration of Poincare duality on stratified singular spaces by using Verdier-self-dual sheaves such as the prototypical intersection chain sheaf on a complex variety.

Topological Invariants of Stratified Spaces Summary

Topological Invariants of Stratified Spaces by Markus Banagl

The central theme of this book is the restoration of Poincare duality on stratified singular spaces by using Verdier-self-dual sheaves such as the prototypical intersection chain sheaf on a complex variety. Highlights include complete and detailed proofs of decomposition theorems for self-dual sheaves, explanation of methods for computing twisted characteristic classes and an introduction to the author's theory of non-Witt spaces and Lagrangian structures.

Topological Invariants of Stratified Spaces Reviews

From the reviews:

This is an excellent book, highly recommended to anyone interested in studying the topology of singular spaces. With modest prerequisites, the author defines intersection homology (both chain- and sheaf-theoretic), gives a self-contained treatment of t-structures and perverse sheaves, and explains the construction as well as algebraic and geometric properties of invariants such as the signature and L-classes associated to self-dual sheaves. (Laurentiu G. Maxim, Mathematical Reviews, Issue 2007 j)

In the book, the construction of these invariants for stratified singular spaces is presented, as well as some methods for their computation. Well written and with modest prerequisites concerning (co)homology theory, simplicial complexes and some basic notions of differential topology, the book is accessible to graduate students. Also, it is useful for the research mathematician wishing to learn about intersection homology and the invariants of singular spaces. (Gheorghe Pitis, Zentralblatt MATH, Vol. 1108 (10), 2007)

About Markus Banagl

EMPLOYMENT: Since 2004: Professor at the Ruprecht-Karls-Universitat Heidelberg, Germany
2002 - 2004: Assistant Professor (tenure track) at the University of Cincinnati, USA
1999 - 2002: Van Vleck Assistant Professor at the University of Wisconsin - Madison, USA

EDUCATION: Ph.D. Mathematics, Courant Institute (New York University), May 1999.
Field: Topology.
Dissertation Title: Extending Intersection Homology Type Invariants to non-Witt Spaces.

RESEARCH AREA: Algebraic and Geometric Topology, Stratified Spaces.

Table of Contents

Elementary Sheaf Theory.- Homological Algebra.- Verdier Duality.- Intersection Homology.- Characteristic Classes and Smooth Manifolds.- Invariants of Witt Spaces.- T-Structures.- Methods of Computation.- Invariants of Non-Witt Spaces.- L2 Cohomology.

Additional information

NPB9783540385851
9783540385851
3540385851
Topological Invariants of Stratified Spaces by Markus Banagl
New
Hardback
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
2007-01-09
264
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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Customer Reviews - Topological Invariants of Stratified Spaces