Topological Invariants of Stratified Spaces

1. Auflage 2007
ISBN: 978-3-540-38585-1
Verlag: Springer

Buch, Englisch, 264 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1250 g

Reihe: Springer Monographs in Mathematics

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.

The book first carefully introduces sheaf theory, derived categories, Verdier duality, stratification theories, intersection homology, t-structures and perverse sheaves. It then explains 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.

Zielgruppe

Research

Autoren/Hrsg.

Banagl, Markus

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Algebraische Topologie

Inhaltsverzeichnis

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.

Über Autor(innen)

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.