Topological Invariants of Stratified Spaces (Springer Monographs in Mathematics)

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9783540385851: Topological Invariants of Stratified Spaces (Springer Monographs in Mathematics)
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The central theme of this book is the restoration of Poincaré 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.

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

After carefully introducing sheaf theory, derived categories,
Verdier duality, stratification theories, intersection homology,
t-structures and perverse sheaves, the ultimate objective is to explain
the construction as well as algebraic and geometric properties of
invariants such as the signature and characteristic classes effectuated
by self-dual sheaves.

Highlights never before presented in book form include complete and
very 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.

About the Author:

EMPLOYMENT: Since 2004: Professor at the Ruprecht-Karls-Universität 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.

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