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External Spanier-Whitehead duality for C-spectra and applications to C-homology theories

dc.contributor.advisorLück, Wolfgang
dc.contributor.authorLackmann, Malte Felix
dc.date.accessioned2021-07-19T13:06:18Z
dc.date.available2021-07-19T13:06:18Z
dc.date.issued19.07.2021
dc.identifier.urihttps://hdl.handle.net/20.500.11811/9229
dc.description.abstractThe 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.en
dc.language.isoeng
dc.rightsIn Copyright
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectRäume über einer Kategorie
dc.subjectC-Homologietheorien
dc.subjectDarstellungssätze
dc.subjectexterne Spanier-Whitehead-Dualität
dc.subjectCherncharakter
dc.subjectspaces over a category
dc.subjectC-homology theories
dc.subjectrepresentation theorems
dc.subjectexternal Spanier-Whitehead duality
dc.subjectChern character
dc.subjectcategory algebra
dc.subjectunique factorisation property
dc.subject.ddc510 Mathematik
dc.titleExternal Spanier-Whitehead duality for C-spectra and applications to C-homology theories
dc.typeDissertation oder Habilitation
dc.publisher.nameUniversitäts- und Landesbibliothek Bonn
dc.publisher.locationBonn
dc.rights.accessRightsopenAccess
dc.identifier.urnhttps://nbn-resolving.org/urn:nbn:de:hbz:5-63002
ulbbn.pubtypeErstveröffentlichung
ulbbnediss.affiliation.nameRheinische Friedrich-Wilhelms-Universität Bonn
ulbbnediss.affiliation.locationBonn
ulbbnediss.thesis.levelDissertation
ulbbnediss.dissID6300
ulbbnediss.date.accepted15.04.2021
ulbbnediss.instituteMathematisch-Naturwissenschaftliche Fakultät : Fachgruppe Mathematik / Mathematisches Institut
ulbbnediss.fakultaetMathematisch-Naturwissenschaftliche Fakultät
dc.contributor.coRefereeSchwede, Stefan
ulbbnediss.contributor.orcidhttps://orcid.org/0000-0002-5115-710X
ulbbn.doiRequestnein


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