Springer Topological Invariants of Stratified Spaces (Springer Monographs in Mathematics)

Product Description 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. Review 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) From the Back Cover The central theme of this book is the restoration of Poincaré dualityon stratified singular spaces by using Verdier-self-dual sheaves suchas 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 explainthe construction as well as algebraic and geometric properties ofinvariants such as the signature and characteristic classes effectuatedby self-dual sheaves. Highlights never before presented in book form include complete andvery detailed proofs of decomposition theorems for self-dual sheaves,explanation of methods for computing twisted characteristic classesand an introduction to the author's theory of non-Witt spaces andLagrangian structures. About the Author EMPLOYMENT: Since 2004: Professor at the Ruprecht-Karls-Universität Heidelberg, Germany2002 - 2004: Assistant Professor (tenure track) at the University of Cincinnati, USA1999 - 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.