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A completion theorem for fusion systems

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Abstract

We show that the twisted K-theory of the classifying space of a p-local finite group is isomorphic to the completion of the Grothendieck group of twisted representations of the fusion system with respect to the augmentation ideal of the representation ring of the fusion system. We use this result to compute the K-theory of the Ruiz-Viruel exotic 7-local finite groups.

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Authors and Affiliations

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

    Noé Bárcenas

  2. A.C. Unidad Mérida Parque Científico y Tecnológico de Yucatán, Consejo Nacional de Ciencia y Tecnología, Centro de Investigación en Matemáticas, Carretera Sierra Papacal-Chuburná Puerto Km 5.5, Mérida, YUC, 97302, Mexico

    José Cantarero

Authors
  1. Noé Bárcenas
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  2. José Cantarero
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Correspondence to José Cantarero.

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Bárcenas, N., Cantarero, J. A completion theorem for fusion systems. Isr. J. Math. 236, 501–531 (2020). https://doi.org/10.1007/s11856-020-1981-4

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  • DOI: https://doi.org/10.1007/s11856-020-1981-4

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