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

Authors:	Egidio Barrera-Yanez Peter B Gilkey

Institution:	(1) Instituto de Matemáticas UNAM U. Cuernavaca, Av. Universidad s/n, Col. Lomas de Chamilpa C.P. 62210, Cuernavaca, Mor. Mexico;(2) Mathematics Department, University of Oregon, Eugene, OR, 97403, U.S.A.;(3) Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22–26, 04103 Leipzig, Germany

Abstract:	We express the real connective K-theory groups $\tilde k$ o_4k–1(B Q ) ofthe quaternion group Q of order = 2^j 8 in terms of therepresentation theory of Q by showing $\tilde k$ o_4k–1(B Q ) = $\tilde K$ Sp(S ^4k+3/Q )where is any fixed point free representation of Q in U(2k + 2).

Keywords:	quaternion spherical space form eta invariant symplectic K-theory real connective K-theory
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