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Transactions of the American Mathematical Society

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Multiplicative structures and the twisted Baum-Connes assembly map


Authors: Noé Bárcenas, Paulo Carrillo Rouse and Mario Velásquez
Journal: Trans. Amer. Math. Soc. 369 (2017), 5241-5269
MSC (2010): Primary 19K56, 19L50; Secondary 46L80
DOI: https://doi.org/10.1090/tran/7024
Published electronically: March 17, 2017
MathSciNet review: 3632567
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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 2003 or by Tu, Xu and Laurent-Gengoux in 2004. These twisted geometric K-homology groups are the left-hand sides of the twisted geometric Baum-Connes assembly maps recently constructed by Carrillo Rouse and Wang (2016), and hence one can transfer the multiplicative structure via the Baum-Connes map to the twisted K-theory groups whenever these assembly maps are isomorphisms.


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Additional Information

Noé Bárcenas
Affiliation: Centro de Ciencias Matemáticas, UNAM, Ap. Postal 61-3 Xangari, Morelia, Michoacán, México 58089
Email: barcenas@matmor.unam.mx

Paulo Carrillo Rouse
Affiliation: Institut de Mathématiques de Toulouse, 118, route de Narbonne, F-31062 Toulouse, France
Email: paulo.carrillo@math.univ-toulouse.fr

Mario Velásquez
Affiliation: Departamento de Matemáticas, Pontificia Universidad Javeriana, Cra. 7, No. 43-82 - Edificio Carlos Ortíz 5to piso, Bogotá D.C, Colombia
Email: mavelasquezm@gmail.com

DOI: https://doi.org/10.1090/tran/7024
Received by editor(s): March 31, 2016
Received by editor(s) in revised form: July 11, 2016
Published electronically: March 17, 2017
Article copyright: © Copyright 2017 American Mathematical Society

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