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Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics)
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Intersection Spaces, Spatial Homology Truncation, and String Theory (Paperback, 2010 ed.)
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Intersection Spaces, Spatial Homology Truncation, and String Theory (Paperback, 2010 ed.)
Series: Lecture Notes in Mathematics, 1997
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Intersection cohomology assigns groups which satisfy a generalized
form of Poincare 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 Poincare 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.
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