On manifold bundles over classifying spaces

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Abstract/Contents

Abstract: This thesis comprises the results of three independent research projects in high-dimensional geometric topology. The first one exhibits, for various manifolds as fibers, smooth bundles over the classifying space of SU(2) not induced from an action. The second project is joint work with M. Krannich. It gives conditions on when a manifold is, up to bordism, the total space of a fiber bundle over a surface with highly-connected and almost-parallelizable fiber M, including a computation of the corresponding characteristic numbers. As a corollary, we determine an explicit basis for the second integral cohomology of BDiff(M) up to torsion in terms of generalized Miller—Morita—Mumford classes. Finally, the third project analyzes models for higher parametrized cobordism categories, with a special focus on the case where the parametrizing space is a circle.

Type of resource	text
Form	electronic resource; remote; computer; online resource
Extent	1 online resource.
Place	California
Place	[Stanford, California]
Publisher	[Stanford University]
Copyright date	2019; ©2019
Publication date	2019; 2019
Issuance	monographic
Language	English

Author	Reinhold, Jens
Degree supervisor	Cohen, Ralph L, 1952-
Degree supervisor	Galatius, Søren, 1976-
Thesis advisor	Cohen, Ralph L, 1952-
Thesis advisor	Galatius, Søren, 1976-
Thesis advisor	Ionel, Eleny
Degree committee member	Ionel, Eleny
Associated with	Stanford University, Department of Mathematics.

Genre	Theses
Genre	Text

Statement of responsibility	Jens Reinhold.
Note	Submitted to the Department of Mathematics.
Thesis	Thesis Ph.D. Stanford University 2019.
Location	electronic resource

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