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A Mayer-Vietoris Spectral Sequence for C*-Algebras and Coarse Geometry

dc.contributor.advisorSchick, Thomas Prof. Dr.
dc.contributor.authorNaarmann, Simon
dc.date.accessioned2019-04-10T09:24:58Z
dc.date.available2019-04-10T09:24:58Z
dc.date.issued2019-04-10
dc.identifier.urihttp://hdl.handle.net/11858/00-1735-0000-002E-E5FF-1
dc.identifier.urihttp://dx.doi.org/10.53846/goediss-7390
dc.language.isoengde
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject.ddc510de
dc.titleA Mayer-Vietoris Spectral Sequence for C*-Algebras and Coarse Geometryde
dc.typedoctoralThesisde
dc.contributor.refereeSchick, Thomas Prof. Dr.
dc.date.examination2018-09-10
dc.description.abstractengLet $A$ be a C*-algebra that is the norm closure $A = \overline{\sum_{\beta \in \alpha} I_\beta}$ of an arbitrary sum of C*-ideals $I_\beta \subseteq A$. We construct a homological spectral sequence that takes as input the K-theory of $\bigcap_{j \in J} I_j$ for all finite nonempty index sets $J \subseteq \alpha$ and converges strongly to the K-theory of $A$. For a coarse space $X$, the Roe algebra $\mathfrak C^* X$ encodes large-scale properties. Given a coarsely excisive cover $\{X_\beta\}_{\beta \in \alpha}$ of $X$, we reshape $\mathfrak C^* X_\beta$ as input for the spectral sequence. From the K-theory of $\mathfrak C^*X \big( \bigcap_{j \in J} X_j \big)$ for finite nonempty index sets $J \subseteq \alpha$, we compute the K-theory of $\mathfrak C^* X$ if $\alpha$ is finite, or of a direct limit C*-ideal of $\mathfrak C^* X$ if $\alpha$ is infinite. Analogous spectral sequences exist for the algebra $\mathfrak D^* X$ of pseudocompact finite-propagation operators that contains the Roe algebra as a C*-ideal, and for $\mathfrak Q^* X = \mathfrak D^* X / \mathfrak C^* X$.de
dc.contributor.coRefereeMeyer, Ralf Prof. Dr.
dc.subject.engK-theoryde
dc.subject.engcoarse geometryde
dc.subject.engMayer-Vietorisde
dc.subject.engspectral sequencede
dc.subject.engC*-algebrade
dc.subject.engRoe algebrade
dc.identifier.urnurn:nbn:de:gbv:7-11858/00-1735-0000-002E-E5FF-1-6
dc.affiliation.instituteFakultät für Mathematik und Informatikde
dc.subject.gokfullMathematics (PPN61756535X)de
dc.identifier.ppn1666650080


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