Concordances in Positive Scalar Curvature and Index Theory

Hertl, Thorsten

dc.contributor.advisor	Schick, Thomas Prof. Dr.
dc.contributor.author	Hertl, Thorsten
dc.date.accessioned	2023-02-24T15:19:01Z
dc.date.available	2023-03-03T00:50:09Z
dc.date.issued	2023-02-24
dc.identifier.uri	http://resolver.sub.uni-goettingen.de/purl?ediss-11858/14542
dc.identifier.uri	http://dx.doi.org/10.53846/goediss-9746
dc.format.extent	256 Seiten	de
dc.language.iso	eng	de
dc.rights.uri	http://creativecommons.org/licenses/by/4.0/
dc.subject.ddc	510	de
dc.title	Concordances in Positive Scalar Curvature and Index Theory	de
dc.type	doctoralThesis	de
dc.contributor.referee	Schick, Thomas Prof. Dr.
dc.date.examination	2022-09-02	de
dc.description.abstracteng	We apply the strategy to study of diffeomorphisms via block diffeomorphisms to the world of positive scalar curvature (psc) metrics. For each closed psc manifold, we construct the cubical set of all psc block metrics, the so called concordance set, which only encodes concordance information of psc metrics within its homotopy type. We show that the concordance is a cubical Kan set, give a geometric description for the group structure of the combinatorial homotopy groups, and construct a comparison map from the cubical model of the space of psc metrics on the underlying manifold to the concordance set. Next, we build a concordance-themed model for real K-theory based on the notion of invertible block Dirac operators and use it to factor the index difference through the concordance set. In the final part of this thesis, we construct the psc Hatcher spectral sequence, which is a non-index-theoretic tool to get information about the difference of the space of psc metrics and the concordance set.	de
dc.contributor.coReferee	Steimle, Wolfgang Prof. Dr.
dc.subject.eng	Positive Scalar Curvature	de
dc.subject.eng	Index Theory	de
dc.subject.eng	Cubical Sets	de
dc.subject.eng	Spectral Sequences	de
dc.subject.eng	Classifying Spaces	de
dc.subject.eng	K-theory	de
dc.subject.eng	Dirac Operators	de
dc.identifier.urn	urn:nbn:de:gbv:7-ediss-14542-7
dc.affiliation.institute	Fakultät für Mathematik und Informatik	de
dc.subject.gokfull	Mathematics (PPN61756535X)	de
dc.description.embargoed	2023-03-03	de
dc.identifier.ppn	1837640335
dc.notes.confirmationsent	Confirmation sent 2023-02-24T15:45:01	de

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Fakultät für Mathematik und Informatik (inkl. GAUSS) [518]

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