| dc.contributor.advisor | Schick, Thomas Prof. Dr. | |
| dc.contributor.author | Nitsche, Martin | |
| dc.date.accessioned | 2018-07-31T09:02:10Z | |
| dc.date.available | 2018-07-31T09:02:10Z | |
| dc.date.issued | 2018-07-31 | |
| dc.identifier.uri | http://hdl.handle.net/11858/00-1735-0000-002E-E464-1 | |
| dc.identifier.uri | http://dx.doi.org/10.53846/goediss-6978 | |
| dc.language.iso | eng | de |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject.ddc | 510 | de |
| dc.title | New topological and index theoretical methods to study the geometry of manifolds | de |
| dc.type | doctoralThesis | de |
| dc.contributor.referee | Schick, Thomas Prof. Dr. | |
| dc.date.examination | 2018-02-06 | |
| dc.description.abstracteng | For a $\mathit{Spin}$ manifold $M$ the Rosenberg index $\alpha([M])$ is an obstruction against positive scalar curvature metrics.
When $M$ is non-$\mathit{Spin}$ but $\mathit{Spin}^c$, Bolotov and Dranishnikov suggested to apply the Rosenberg index to a suitable $S^1$-bundle $L\to M$.
We study this approach, in particular for the case $\pi_1(L)\neq\pi_1(M)$. We explain how the bundle construction can be turned into a non-trivial natural transformation of bordism groups $\Omega^{\mathit{Spin}^c}\to\Omega^\mathit{Spin}$. Then we show that $\alpha([L])\in\mathit{KO}(C^*(\pi_1(L)))$ always vanishes, but also give an example where $L$ nonetheless does not admit a positive scalar curvature metric. The second part of the thesis concerns the relation of $\alpha([N])$ and $\alpha([M])$
for certain codimension-2 submanifolds $N\subset M$.
Following a construction of Engel we extend the Thom map $\mathit{KO}_*(M)\to\mathit{KO}_{*-2}(N)$ to $\mathit{KO}_*(\mathbf{B}\pi_1(M))\to\mathit{KO}_{*-2}(\mathbf{B}\pi_1(N))$,
and then further to $\mathit{KO}_*^{\pi_1(M)}(\mathbf{\underline{E}}\pi_1(M))\to\mathit{KO}_{*-2}^{\pi_1(N)}(\mathbf{\underline{E}}\pi_1(N))$. | de |
| dc.contributor.coReferee | Meyer, Ralf Prof. Dr. | |
| dc.contributor.thirdReferee | Bahns, Dorothea Prof. Dr. | |
| dc.contributor.thirdReferee | Pidstrygach, Viktor Prof. Dr. | |
| dc.contributor.thirdReferee | Rehren, Karl-Henning Prof. Dr. | |
| dc.contributor.thirdReferee | Wardetzky, Max Prof. Dr. | |
| dc.subject.eng | positive scalar curvature | de |
| dc.subject.eng | Rosenberg index | de |
| dc.subject.eng | geometric K-homology | de |
| dc.subject.eng | circle bundle | de |
| dc.subject.eng | classifying space for proper actions | de |
| dc.subject.eng | codimension-2 transfer | de |
| dc.subject.eng | Spin^c | de |
| dc.identifier.urn | urn:nbn:de:gbv:7-11858/00-1735-0000-002E-E464-1-8 | |
| dc.affiliation.institute | Fakultät für Mathematik und Informatik | de |
| dc.subject.gokfull | Mathematics (PPN61756535X) | de |
| dc.identifier.ppn | 1028021313 | |