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dc.contributor.authorProietti, Valerio
dc.contributor.authorYamashita, Makoto
dc.date.accessioned2020-10-09T09:43:09Z
dc.date.available2020-10-09T09:43:09Z
dc.date.issued2020-10-09
dc.identifier.urihttp://publications.mfo.de/handle/mfo/3800
dc.description.abstractGiven an ample groupoid, we construct a spectral sequence with groupoid homology with integer coefficients on the second sheet, converging to the $K$-groups of the groupoid C*-algebra when the groupoid has torsion-free stabilizers and satisfies the strong Baum–Connes conjecture. The construction is based on the triangulated category approach to the Baum–Connes conjecture by Meyer and Nest. For the unstable equivalence relation of a Smale space with totally disconnected stable sets, this spectral sequence shows Putnam’s homology groups on the second sheet.en_US
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints, 2020-20
dc.subjectGroupoiden_US
dc.subjectC*-algebraen_US
dc.subjectK-theoryen_US
dc.subjectHomologyen_US
dc.subjectBaum-Connes conjectureen_US
dc.subjectSmale spaceen_US
dc.titleHomology and $K$-Theory of Torsion-Free Ample Groupoids and Smale Spacesen_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2020-20
local.scientificprogramOWLF 2020en_US
local.series.idOWP-2020-20en_US
local.subject.msc46en_US
local.subject.msc19en_US
local.subject.msc37en_US


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