Ring structures in coarse K-theory
- The K-theory of the stable Higson corona of a coarse space carries a canonical ring structure. The present thesis covers two aspects of this ring: Chapter 1: The K-theory of the stable Higson corona is the domain of an unreduced version of the coarse co-assembly map of Emerson and Meyer. We show that the target also carries a ring structure and co-assembly is a ring homomorphism, provided that the given coarse space is contractible in a coarse sense. Chapter 2 (pursuing conjectures of John Roe): Applied to a foliated cone over a foliation, we show that the K-theory of the stable Higson corona can be considered as a new model for the K-theory of the leaf space, which is - in contrast to Connes' K-theory model - a ring. We show that Connes' K-theory model is a module over this ring and develop an interpretation of the module structure in terms of twisted longitudinally elliptic operators.
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| Author: | Christopher Wulff |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-31655 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/3165 |
| Advisor: | Bernhard Hanke |
| Type: | Doctoral Thesis |
| Language: | English |
| Publishing Institution: | Universität Augsburg |
| Granting Institution: | Universität Augsburg, Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Date of final exam: | 2015/06/25 |
| Release Date: | 2015/08/26 |
| Tag: | coarse geometry; co-assembly; K-theory; foliation index theory; ring and module structures |
| GND-Keyword: | K-Theorie; Indextheorie; Ringstruktur |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  Deutsches Urheberrecht mit Print on Demand |
