2015/01/21 by Noé Bárcenas, Bárcenas, Noé, Paulo Carrillo Rouse +3
Mathematics · #FOS: Mathematics #K-Theory and Homology (math.KT) #math.KT
paper · pdf · doi:10.48550/arxiv.1501.05255
27 pages. We thank the collegue that revised a previous version of this paper for his accurate comments and remarks that allow us to correct some imprecisions and clarify and improve the contents of this work
arxiv created 2016/03/30 · arxiv updated 2016/03/31
Using a combination of Atiyah-Segal ideas on one side and of Connes and Baum-Connes ideas on the other, we prove that the Twisted geometric K-homology groups of a Lie groupoid have an external multiplicative structure extending hence the external product structures for proper cases considered by Adem-Ruan in [1] or by Tu,Xu and Laurent-Gengoux in [24]. These Twisted geometric K-homology groups are the left hand sides of the twisted geometric Baum-Connes assembly maps recently constructed in [9] and hence one can transfer the multiplicative structure via the Baum-Connes map to the Twisted K-theory groups whenever this assembly maps are isomorphisms.