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2002
Issue 83

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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 $\tilde{k} o_{4 k - 1} (B Q_{ℓ})$ of the quaternion group $Q_{ℓ}$ of order $ℓ = 2^{j} \geq 8$ in terms of the representation theory of $Q_{ℓ}$ by showing $\tilde{k} o_{4 k - 1} (B Q_{ℓ}) = \tilde{K} S p (S^{4 k + 3} / τ Q_{ℓ})$ where $τ$ is any fixed point free representation of $Q_{ℓ}$ in $U (2 k + 2)$ .

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Received:: 10.09.02

Published:: 10.09.02

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

BibTex DOI: 10.1023/A:1022488431610