Topological and Piecewise Linear Pseudoisotopy Functors
Topological and Piecewise Linear Pseudoisotopy Functors
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DissertationPrüfungsdatum
30.01.2019Datum der Veröffentlichung
16.05.2019Erstgutachter
Lück, WolfgangZweitgutachter
Steimle, WolfgangMetadaten
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Inhalt
We construct two functors Pstrict∂:Top →Top and ℙstrict∂:Top → Spectra such that for a compact manifold M the space Pstrict∂(M) has the homotopy type of the stable topological pseudoisotopy space of M and ℙstrict∂(M) has the homotopy type of the topological pseudoisotopy spectrum of M. Both functors also induce homotopy functors that agree with the homotopy functor defined by Hatcher in 1978. The main idea of the construction is to build a homotopy coherent diagram out of induced maps as defined by Hatcher, then strictify the diagram and finally use a left Kan extension to extend the domain of the functor to the whole category Top of topological spaces. Our construction generalizes to the piecewise linear category and also yields piecewise linear versions of the two functors.
The functor Pstrict∂ was already used in the work of other authors, although no complete construction of it existed prior to this work. We aim to close this gap in the literature.
The functor Pstrict∂ was already used in the work of other authors, although no complete construction of it existed prior to this work. We aim to close this gap in the literature.
Schlagwörter
Homotopietheorie, Homotopiefunktor, Pseudoisotopie, Spektren, Topologische Mannigfaltigkeiten, stückweise lineare Mannigfaltigkeiten, homotopy theory, homotopy functors, pseudo-isotopy, spectra, topological manifolds, piecewise-linear manifolds
Klassifikation (DDC)
510 MathematikEnkelmann, Nils-Edvin: Topological and Piecewise Linear Pseudoisotopy Functors. - Bonn, 2019. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-54308
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-54308
@phdthesis{handle:20.500.11811/7911,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-54308,
author = {{Nils-Edvin Enkelmann}},
title = {Topological and Piecewise Linear Pseudoisotopy Functors},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2019,
month = may,
note = {We construct two functors Pstrict∂:Top →Top and ℙstrict∂:Top → Spectra such that for a compact manifold M the space Pstrict∂(M) has the homotopy type of the stable topological pseudoisotopy space of M and ℙstrict∂(M) has the homotopy type of the topological pseudoisotopy spectrum of M. Both functors also induce homotopy functors that agree with the homotopy functor defined by Hatcher in 1978. The main idea of the construction is to build a homotopy coherent diagram out of induced maps as defined by Hatcher, then strictify the diagram and finally use a left Kan extension to extend the domain of the functor to the whole category Top of topological spaces. Our construction generalizes to the piecewise linear category and also yields piecewise linear versions of the two functors.
The functor Pstrict∂ was already used in the work of other authors, although no complete construction of it existed prior to this work. We aim to close this gap in the literature.},
url = {https://hdl.handle.net/20.500.11811/7911}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-54308,
author = {{Nils-Edvin Enkelmann}},
title = {Topological and Piecewise Linear Pseudoisotopy Functors},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2019,
month = may,
note = {We construct two functors Pstrict∂:Top →Top and ℙstrict∂:Top → Spectra such that for a compact manifold M the space Pstrict∂(M) has the homotopy type of the stable topological pseudoisotopy space of M and ℙstrict∂(M) has the homotopy type of the topological pseudoisotopy spectrum of M. Both functors also induce homotopy functors that agree with the homotopy functor defined by Hatcher in 1978. The main idea of the construction is to build a homotopy coherent diagram out of induced maps as defined by Hatcher, then strictify the diagram and finally use a left Kan extension to extend the domain of the functor to the whole category Top of topological spaces. Our construction generalizes to the piecewise linear category and also yields piecewise linear versions of the two functors.
The functor Pstrict∂ was already used in the work of other authors, although no complete construction of it existed prior to this work. We aim to close this gap in the literature.},
url = {https://hdl.handle.net/20.500.11811/7911}
}
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