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The completion theorem in twisted equivariant K-theory for proper actions

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Abstract

We compare different algebraic structures in twisted equivariant K-theory for proper actions of discrete groups. After the construction of a module structure over untwisted equivariant K-theory, we prove a completion Theorem of Atiyah–Segal type for twisted equivariant K-theory. Using a universal coefficient theorem, we prove a cocompletion Theorem for twisted Borel K-homology for discrete groups.

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Acknowledgements

The first author thanks the support of PAPIIT research grant IA100315.

The second author thanks partial support of a UNAM Postdoctoral Fellowship.

The first and second author thank Université Toulouse III Paul Sabatier, as well as the Laboratoire International Solomon Lefschetz (LAISLA) for support during a visit to Toulouse, where parts of this work were written.

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Authors and Affiliations

  1. Centro de Ciencias Matemáticas, UNAM, Ap. Postal 61-3 Xangari, 58089, Morelia, Michoacán, Mexico

    Noé Bárcenas

  2. Sede Bogotá, Facultad de Ciencias, Departamento de Matemáticas, Universidad Nacional de Colombia, Cra. 30 cll 45-Ciudad Universitaria, Bogotá, Colombia

    Mario Velásquez

Authors
  1. Noé Bárcenas
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  2. Mario Velásquez
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Correspondence to Mario Velásquez.

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Communicated by Thomas Schick.

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Bárcenas, N., Velásquez, M. The completion theorem in twisted equivariant K-theory for proper actions. J. Homotopy Relat. Struct. 17, 77–104 (2022). https://doi.org/10.1007/s40062-021-00299-z

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