On the Classification of Cohomology Bott Manifolds
On the Classification of Cohomology Bott Manifolds
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DissertationDate of Exam
27.09.2013Date of Publication
07.11.2013Advisor
Kreck, MatthiasCo-Referee
Laures, GerdMetadata
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Abstract
We study cohomology Bott manifolds by means of modified surgery theory. Cohomology Bott manifolds admit a ring isomorphism to the cohomology ring of a Bott manifold which preserves the Pontrjagin and Stiefel-Whitney classes. We show that the number of diffeomorphism classes of cohomology Bott manifolds is finite and construct first examples of manifolds which are cohomology Bott manifolds but not Bott manifolds. Furthermore, we consider the strong cohomological rigidity problem, i.e. we examine the realisability question for an automorphism of the cohomology ring of a specific Bott manifold.
Subjects
Differentialtopologie, Chirurgietheorie, Bordismus, Diffeomorphismen, algebraische Topologie, differentiable topology, surgery theory, bordism, diffeomorphisms, algebraic topology
Classification (DDC)
510 MathematikAbczynski, Anna: On the Classification of Cohomology Bott Manifolds. - Bonn, 2013. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-33661
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-33661
@phdthesis{handle:20.500.11811/5771,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-33661,
author = {{Anna Abczynski}},
title = {On the Classification of Cohomology Bott Manifolds},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2013,
month = nov,
note = {We study cohomology Bott manifolds by means of modified surgery theory. Cohomology Bott manifolds admit a ring isomorphism to the cohomology ring of a Bott manifold which preserves the Pontrjagin and Stiefel-Whitney classes. We show that the number of diffeomorphism classes of cohomology Bott manifolds is finite and construct first examples of manifolds which are cohomology Bott manifolds but not Bott manifolds. Furthermore, we consider the strong cohomological rigidity problem, i.e. we examine the realisability question for an automorphism of the cohomology ring of a specific Bott manifold.},
url = {https://hdl.handle.net/20.500.11811/5771}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-33661,
author = {{Anna Abczynski}},
title = {On the Classification of Cohomology Bott Manifolds},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2013,
month = nov,
note = {We study cohomology Bott manifolds by means of modified surgery theory. Cohomology Bott manifolds admit a ring isomorphism to the cohomology ring of a Bott manifold which preserves the Pontrjagin and Stiefel-Whitney classes. We show that the number of diffeomorphism classes of cohomology Bott manifolds is finite and construct first examples of manifolds which are cohomology Bott manifolds but not Bott manifolds. Furthermore, we consider the strong cohomological rigidity problem, i.e. we examine the realisability question for an automorphism of the cohomology ring of a specific Bott manifold.},
url = {https://hdl.handle.net/20.500.11811/5771}
}
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