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MiS Preprint
83/2002

The eta invariant and the real connective K-theory of the classifying space for quaternion groups

Egidio Barrera-Yanez and Peter B. Gilkey

Abstract

We express the real connective $K$ theory groups $\tilde ko_{4k-1}(BQ_\ell)$ of the quaternion group $Q_\ell$ of order $\ell=2^j\ge8$ in terms of the representation theory of $Q_\ell$ by showing $\tilde ko_{4k-1}(BQ_\ell)=\tilde KSp(S^{4k+3}/\tau Q_\ell)$ where $\tau$ is any fixed point free representation of $Q_\ell$ in $U(2k+2)$.

Received:
Sep 10, 2002
Published:
Sep 10, 2002
MSC Codes:
58G25
Keywords:
quaternion spherical space form, eta invariant, symplectic k theory, real connective k theory

Related publications

inJournal
2003 Repository Open Access
Peter B. Gilkey and Egidio Barrera-Yanez

The eta invariant and the real connective K-theory of the classifying space for quaternion groups

In: Annals of global analysis and geometry, 23 (2003) 2, pp. 173-188