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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 $U(2k+2)$.
