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Intersection Spaces, Spatial Homology Truncation, and String Theory

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  • © 2010

Overview

Authors:
  1. Markus Banagl

    1. Mathematics Institute, University of Heidelberg, Heidelberg, Germany

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

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Table of contents (3 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Homotopy Theory

    • Markus Banagl
    Pages 1-106

  3. Intersection Spaces

    • Markus Banagl
    Pages 107-189

  4. String Theory

    • Markus Banagl
    Pages 191-209

  5. Back Matter

    Pages 211-223
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Keywords

About this book

Intersection cohomology assigns groups which satisfy a generalized form of Poincaré duality over the rationals to a stratified singular space. This 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 tohomotopy 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.

Authors and Affiliations

  • Mathematics Institute, University of Heidelberg, Heidelberg, Germany

    Markus Banagl

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