dc.contributor.author | Nishikawa, Shintaro | |
dc.contributor.author | Proietti, Valerio | |
dc.date.accessioned | 2019-09-17T12:02:26Z | |
dc.date.available | 2019-09-17T12:02:26Z | |
dc.date.issued | 2019-09-17 | |
dc.identifier.uri | http://publications.mfo.de/handle/mfo/2518 | |
dc.description.abstract | We introduce the notion of Spanier-Whitehead $K$-duality for a discrete group $G$, 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. | en_US |
dc.language.iso | en_US | en_US |
dc.publisher | Mathematisches Forschungsinstitut Oberwolfach | en_US |
dc.relation.ispartofseries | Oberwolfach Preprints;2019,23 | |
dc.subject | Spanier-Whitehead duality | en_US |
dc.subject | Poincaré duality | en_US |
dc.subject | Baum-Connes conjecture | en_US |
dc.subject | Direct splitting method | en_US |
dc.subject | Noncommutative topology | en_US |
dc.title | Groups with Spanier-Whitehead Duality | en_US |
dc.type | Preprint | en_US |
dc.identifier.doi | 10.14760/OWP-2019-23 | |
local.scientificprogram | OWLF 2019 | en_US |
local.series.id | OWP-2019-23 | en_US |
local.subject.msc | 46 | en_US |
local.subject.msc | 55 | en_US |