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dc.contributor.authorNishikawa, Shintaro
dc.contributor.authorProietti, Valerio
dc.date.accessioned2019-09-17T12:02:26Z
dc.date.available2019-09-17T12:02:26Z
dc.date.issued2019-09-17
dc.identifier.urihttp://publications.mfo.de/handle/mfo/2518
dc.description.abstractWe 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.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2019,23
dc.subjectSpanier-Whitehead dualityen_US
dc.subjectPoincaré dualityen_US
dc.subjectBaum-Connes conjectureen_US
dc.subjectDirect splitting methoden_US
dc.subjectNoncommutative topologyen_US
dc.titleGroups with Spanier-Whitehead Dualityen_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2019-23
local.scientificprogramOWLF 2019en_US
local.series.idOWP-2019-23en_US
local.subject.msc46en_US
local.subject.msc55en_US


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