Markus Banagl

Topological Invariants of Stratified Spaces (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 264
• Erscheinungstermin: 16. Februar 2007
• Englisch
• ISBN-13: 9783540385875
• Artikelnr.: 37368252

Autorenporträt

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.

Inhaltsangabe

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.

Rezensionen

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)