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

arXiv:math/0205084

Abstract

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