| dc.contributor.advisor | Schick, Thomas Prof. Dr. | |
| dc.contributor.author | Naarmann, Simon | |
| dc.date.accessioned | 2019-04-10T09:24:58Z | |
| dc.date.available | 2019-04-10T09:24:58Z | |
| dc.date.issued | 2019-04-10 | |
| dc.identifier.uri | http://hdl.handle.net/11858/00-1735-0000-002E-E5FF-1 | |
| dc.identifier.uri | http://dx.doi.org/10.53846/goediss-7390 | |
| dc.language.iso | eng | de |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject.ddc | 510 | de |
| dc.title | A Mayer-Vietoris Spectral Sequence for C*-Algebras and Coarse Geometry | de |
| dc.type | doctoralThesis | de |
| dc.contributor.referee | Schick, Thomas Prof. Dr. | |
| dc.date.examination | 2018-09-10 | |
| dc.description.abstracteng | Let $A$ 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.coReferee | Meyer, Ralf Prof. Dr. | |
| dc.subject.eng | K-theory | de |
| dc.subject.eng | coarse geometry | de |
| dc.subject.eng | Mayer-Vietoris | de |
| dc.subject.eng | spectral sequence | de |
| dc.subject.eng | C*-algebra | de |
| dc.subject.eng | Roe algebra | de |
| dc.identifier.urn | urn:nbn:de:gbv:7-11858/00-1735-0000-002E-E5FF-1-6 | |
| dc.affiliation.institute | Fakultät für Mathematik und Informatik | de |
| dc.subject.gokfull | Mathematics (PPN61756535X) | de |
| dc.identifier.ppn | 1666650080 | |