Intersection Spaces, Spatial Homology Truncation, and String Theory

• Main Author: Banagl, Markus. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.
• Series: Lecture Notes in Mathematics, 1997
• Subjects: Mathematics.; Geometry, algebraic.; Topology.; Algebraic topology.; Cell aggregation > Mathematics.; Mathematical physics.; Algebraic Geometry.; Algebraic Topology.; Manifolds and Cell Complexes (incl. Diff.Topology).; Quantum Field Theories, String Theory.; Mathematical Methods in Physics.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-12589-8

 Intersection cohomology assigns groups which satisfy a generalized form of Poincar ̌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 Poincar ̌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.