English

Multiplicative Structures and the Twisted Baum-Connes Assembly map

K-Theory and Homology 2016-03-31 v2

Abstract

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.

Keywords

Cite

@article{arxiv.1501.05255,
  title  = {Multiplicative Structures and the Twisted Baum-Connes Assembly map},
  author = {Noé Bárcenas and Paulo Carrillo Rouse and Mario Velásquez},
  journal= {arXiv preprint arXiv:1501.05255},
  year   = {2016}
}

Comments

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

R2 v1 2026-06-22T08:08:48.396Z