External Spanier-Whitehead duality for C-spectra and applications to C-homology theories
External Spanier-Whitehead duality for C-spectra and applications to C-homology theories
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DissertationPrüfungsdatum
15.04.2021Datum der Veröffentlichung
19.07.2021Erstgutachter
Lück, WolfgangZweitgutachter
Schwede, StefanMetadaten
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Inhalt
The thesis constructs a Spanier-Whitehead type duality functor relating finite C-spectra to finite Cop-spectra, where C is a topological index category. We prove that every C-homology theory is given by taking the homotopy groups of a balanced smash product with a fixed Cop-spectrum. As an application, we construct Chern characters for certain rational C-homology theories. The existence of Chern characters leads to the algebraic question of the hereditarity of category algebras for which a complete characterisation is given. A particular focus is set on the case of orbit categories.
Schlagwörter
Räume über einer Kategorie, C-Homologietheorien, Darstellungssätze, externe Spanier-Whitehead-Dualität, Cherncharakter, spaces over a category, C-homology theories, representation theorems, external Spanier-Whitehead duality, Chern character, category algebra, unique factorisation property
Klassifikation (DDC)
510 MathematikLackmann, Malte Felix: External Spanier-Whitehead duality for C-spectra and applications to C-homology theories. - Bonn, 2021. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5-63002
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5-63002
@phdthesis{handle:20.500.11811/9229,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5-63002,
author = {{Malte Felix Lackmann}},
title = {External Spanier-Whitehead duality for C-spectra and applications to C-homology theories},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2021,
month = jul,
note = {The thesis constructs a Spanier-Whitehead type duality functor relating finite C-spectra to finite Cop-spectra, where C is a topological index category. We prove that every C-homology theory is given by taking the homotopy groups of a balanced smash product with a fixed Cop-spectrum. As an application, we construct Chern characters for certain rational C-homology theories. The existence of Chern characters leads to the algebraic question of the hereditarity of category algebras for which a complete characterisation is given. A particular focus is set on the case of orbit categories.},
url = {https://hdl.handle.net/20.500.11811/9229}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5-63002,
author = {{Malte Felix Lackmann}},
title = {External Spanier-Whitehead duality for C-spectra and applications to C-homology theories},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2021,
month = jul,
note = {The thesis constructs a Spanier-Whitehead type duality functor relating finite C-spectra to finite Cop-spectra, where C is a topological index category. We prove that every C-homology theory is given by taking the homotopy groups of a balanced smash product with a fixed Cop-spectrum. As an application, we construct Chern characters for certain rational C-homology theories. The existence of Chern characters leads to the algebraic question of the hereditarity of category algebras for which a complete characterisation is given. A particular focus is set on the case of orbit categories.},
url = {https://hdl.handle.net/20.500.11811/9229}
}
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