Eintrag in der Universitätsbibliographie der TU Chemnitz
Volltext zugänglich unter
URN: urn:nbn:de:bsz:ch1-qucosa2-910433
Miehe, Jonas Philipp
Güneysu, Batu (Prof. Dr.) ; Cacciatori, Sergio (Prof. Dr.) ; Shen, Shu (Dr.) (Gutachter)
The Chern character of theta-summable Cq-Fredholm modules
Kurzfassung in englisch
In this thesis, we develop a framework that generalizes the previously known notions of theta-summable Fredholm modules to the setting of locally convex dg algebras. By introducing an additional action of the Clifford algebra, we may treat the even and odd cases simultaneously. In particular, we recover the theory developed by Güneysu/Ludewig and extend the definition of odd theta-summable Fredholm modules to the differential graded category. We then construct a Chern character, which serves as a differential graded refinement of the JLO cocycle, and prove that it has all the expected analytical and homological properties. As an application, we prove an odd noncommutative index theorem relating the spectral flow of a theta-summable Fredholm module to the pairing of the Chern character with the odd Bismut-Chern character in entire (differential graded) cyclic homology, thereby extending results obtained by Güneysu/Cacciatori and Getzler.
| Universität: | Technische Universität Chemnitz | |
| Institut: | Professur Analysis (Güneysu) | |
| Fakultät: | Fakultät für Mathematik | |
| Dokumentart: | Dissertation | |
| Betreuer: | Güneysu, Batu (Prof. Dr.) | |
| URL/URN: | https://nbn-resolving.org/urn:nbn:de:bsz:ch1-qucosa2-910433 | |
| SWD-Schlagwörter: | Nichtkommutative Geometrie , Zyklische Homologie | |
| Freie Schlagwörter (Englisch): | noncommutative geometry , cyclic homology , functional analysis , spectral triples , dg algebras | |
| DDC-Sachgruppe: | Geometrie, Analysis, Algebra, Mathematik | |
| Sprache: | englisch | |
| Tag der mündlichen Prüfung | 08.04.2024 | |
| OA-Lizenz | CC BY 4.0 |
