Homological Stability, Characteristic Classes and the Minimal Genus Problem
Homological Stability, Characteristic Classes and the Minimal Genus Problem
View/Type of Scholarly Publication
DissertationDate of Exam
14.12.2020Date of Publication
07.04.2021Advisor
Hamenstädt, UrsulaCo-Referee
Lück, WolfgangMetadata
Show full item record
Citable Links 
Abstract
The purpose of this thesis is to study the (co-)homological properties of the classifying space of subsurface bundles in a trivial background bundle with fiber a manifold M. We will investigate homological stability pheonomena of this moduli space if M is simply-connected and at least 5-dimensional and the subsurfaces are equipped with tangential structures. Additionally we will investigate the representability of second homology classes by surfaces in general topological spaces. In the case of manifolds this yields a measure for the failure of homological stability if M is not simply-connected. In the introduction we will also briefly touch on how to proceed from these homological stability results to determining the stable characteristic classes of subsurface bundles.
Classification (DDC)
510 MathematikKastenholz, Thorben Gerhard: Homological Stability, Characteristic Classes and the Minimal Genus Problem. - Bonn, 2021. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5-61233
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5-61233
@phdthesis{handle:20.500.11811/9027,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5-61233,
author = {{Thorben Gerhard Kastenholz}},
title = {Homological Stability, Characteristic Classes and the Minimal Genus Problem},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2021,
month = apr,
note = {The purpose of this thesis is to study the (co-)homological properties of the classifying space of subsurface bundles in a trivial background bundle with fiber a manifold M. We will investigate homological stability pheonomena of this moduli space if M is simply-connected and at least 5-dimensional and the subsurfaces are equipped with tangential structures. Additionally we will investigate the representability of second homology classes by surfaces in general topological spaces. In the case of manifolds this yields a measure for the failure of homological stability if M is not simply-connected. In the introduction we will also briefly touch on how to proceed from these homological stability results to determining the stable characteristic classes of subsurface bundles.},
url = {https://hdl.handle.net/20.500.11811/9027}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5-61233,
author = {{Thorben Gerhard Kastenholz}},
title = {Homological Stability, Characteristic Classes and the Minimal Genus Problem},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2021,
month = apr,
note = {The purpose of this thesis is to study the (co-)homological properties of the classifying space of subsurface bundles in a trivial background bundle with fiber a manifold M. We will investigate homological stability pheonomena of this moduli space if M is simply-connected and at least 5-dimensional and the subsurfaces are equipped with tangential structures. Additionally we will investigate the representability of second homology classes by surfaces in general topological spaces. In the case of manifolds this yields a measure for the failure of homological stability if M is not simply-connected. In the introduction we will also briefly touch on how to proceed from these homological stability results to determining the stable characteristic classes of subsurface bundles.},
url = {https://hdl.handle.net/20.500.11811/9027}
}
The following license files are associated with this item:
