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arXiv · 1501.05255

Multiplicative Structures and the Twisted Baum-Connes Assembly map

Noé Bárcenas·Paulo Carrillo Rouse·Mario Velásquez
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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.

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Noé Bárcenas, Paulo Carrillo Rouse, Mario Velásquez. 2016-03-30. Multiplicative Structures and the Twisted Baum-Connes Assembly map. https://arxiv.org/abs/1501.05255

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