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Dissertation/Thesis Abstract

Cobordism categories, corners, and surgery
by Genauer, Josh, Ph.D., Stanford University, 2009, 78; 3364500
Abstract (Summary)

The first result of this manuscript is a formula for calculating the homotopy type of the classifying space of the cobordism category [special characters omitted] the cobordism category whose morphisms are cobordisms of manifolds of fixed dimension d with corners of codimension ≤ k together with structure on the tangent bundle determined by a fibration &thetas;. The result is the zero space of a homotopy colimit over a certain diagram of Thom spectra. In some interesting cases we are able to evaluate this homotopy colimit explicitly. One such case is the cobordism category of oriented two-dimensional manifolds with boundary. In other words, we determine the homotopy type of the domain of an open-closed topological field theory.

The second half of this thesis shows how the traditional sets appearing in the Browder-Novikov-Sullivan-Wall smooth surgery sequence may be replaced by the classifying spaces of cobordism categories and the maps between these sets may be replaced by functors.

Indexing (document details)
Advisor: Cohen, Ralph L.
School: Stanford University
School Location: United States -- California
Source: DAI-B 70/07, Dissertation Abstracts International
Subjects: Mathematics
Keywords: Cobordism, Homotopy types, Smooth surgery sequence
Publication Number: 3364500
ISBN: 978-1-109-24288-1
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