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The Eta Invariant and the Real Connective K-Theory of the Classifying Space for Quaternion Groups

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Abstract

We express the real connective K-theory groups \(\tilde k\)o4k−1(B Q ℓ) ofthe quaternion group Q ℓof order ℓ = 2j ≥ 8 in terms of therepresentation theory of Q ℓ by showing \(\tilde k\)o4k−1(B Q ℓ) = \(\tilde K\)Sp(S 4k+3/τQ ℓ)where τ is any fixed point free representation of Q ℓin U(2k + 2).

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Authors and Affiliations

  1. Instituto de Matemáticas UNAM U. Cuernavaca, Av. Universidad s/n, Col. Lomas de Chamilpa C.P. 62210, Cuernavaca, Mor. Mexico

    Egidio Barrera-Yanez

  2. Mathematics Department, University of Oregon, Eugene, OR, 97403, U.S.A.

    Peter B. Gilkey

  3. Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22–26, 04103, Leipzig, Germany

    Peter B. Gilkey

Authors
  1. Egidio Barrera-Yanez
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  2. Peter B. Gilkey
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Barrera-Yanez, E., Gilkey, P.B. The Eta Invariant and the Real Connective K-Theory of the Classifying Space for Quaternion Groups. Annals of Global Analysis and Geometry 23, 173–188 (2003). https://doi.org/10.1023/A:1022488431610

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