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Intersection Spaces, Spatial Homology Truncation, and String Theory

  • Markus Banagl

Part of the Lecture Notes in Mathematics book series (LNM, volume 1997)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Markus Banagl
    Pages 1-106
  3. Markus Banagl
    Pages 107-189
  4. Markus Banagl
    Pages 191-209
  5. Back Matter
    Pages 211-223

About this book

Introduction

Intersection cohomology assigns groups which satisfy a generalized form of Poincaré duality over the rationals to a stratified singular space. The present monograph introduces a method that assigns to certain classes of stratified spaces cell complexes, called intersection spaces, whose ordinary rational homology satisfies generalized Poincaré duality. The cornerstone of the method is a process of spatial homology truncation, whose functoriality properties are analyzed in detail. The material on truncation is autonomous and may be of independent interest to homotopy theorists. The cohomology of intersection spaces is not isomorphic to intersection cohomology and possesses algebraic features such as perversity-internal cup-products and cohomology operations that are not generally available for intersection cohomology. A mirror-symmetric interpretation, as well as applications to string theory concerning massless D-branes arising in type IIB theory during a Calabi-Yau conifold transition, are discussed.

Keywords

Homotopy Homotopy Theory Intersection homology K-theory Singularities Stratified Spaces String Theory cohomology homology vector bundle

Authors and affiliations

  • Markus Banagl
    • 1
  1. 1.Mathematics InstituteUniversity of HeidelbergHeidelbergGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-12589-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-12588-1
  • Online ISBN 978-3-642-12589-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site