, Volume 37, Issue 3, pp 275-306
Date: 29 Nov 2009

The eta invariant and equivariant bordism of flat manifolds with cyclic holonomy group of odd prime order

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Abstract

We study the eta invariants of compact flat spin manifolds of dimension n with holonomy group \({\mathbb{Z}_p}\) , where p is an odd prime. We find explicit expressions for the twisted and relative eta invariants and show that the reduced eta invariant is always an integer, except in a single case, when p = n = 3. We use the expressions obtained to show that any such manifold is trivial in the appropriate reduced equivariant spin bordism group.

Peter B. Gilkey partially supported by Project MTM2006-01432 (Spain), and Roberto J. Miatello, Ricardo A. Podestá partially supported by CONICET, Foncyt, and SECyT-UNC.