Groups with Spanier-Whitehead duality
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2019
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916540316647424 |
|---|---|
| author | Nishikawa, Shintaro Proietti, Valerio |
| author_facet | Nishikawa, Shintaro Proietti, Valerio |
| contents | Building on work by Kasparov, we study the notion of Spanier-Whitehead K-duality for a discrete group. It is defined as duality in the KK-category between two C*-algebras which are naturally attached to the group, namely the reduced group C*-algebra and the crossed product for the group action on the universal example for proper actions. We compare this notion to the Baum-Connes conjecture by constructing duality classes based on two methods: the standard "gamma element" technique, and the more recent approach via cycles with property gamma. As a result of our analysis, we prove Spanier-Whitehead duality for a large class of groups, including Bieberbach's space groups, groups acting on trees, and lattices in Lorentz groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1908_03749 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Groups with Spanier-Whitehead duality Nishikawa, Shintaro Proietti, Valerio K-Theory and Homology Operator Algebras 46L85 (Primary) 46L80, 55P25 (Secondary) Building on work by Kasparov, we study the notion of Spanier-Whitehead K-duality for a discrete group. It is defined as duality in the KK-category between two C*-algebras which are naturally attached to the group, namely the reduced group C*-algebra and the crossed product for the group action on the universal example for proper actions. We compare this notion to the Baum-Connes conjecture by constructing duality classes based on two methods: the standard "gamma element" technique, and the more recent approach via cycles with property gamma. As a result of our analysis, we prove Spanier-Whitehead duality for a large class of groups, including Bieberbach's space groups, groups acting on trees, and lattices in Lorentz groups. |
| title | Groups with Spanier-Whitehead duality |
| topic | K-Theory and Homology Operator Algebras 46L85 (Primary) 46L80, 55P25 (Secondary) |
| url | https://arxiv.org/abs/1908.03749 |