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.
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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.
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Gilkey, P.B., Miatello, R.J. & Podestá, R.A. The eta invariant and equivariant bordism of flat manifolds with cyclic holonomy group of odd prime order. Ann Glob Anal Geom 37, 275–306 (2010). https://doi.org/10.1007/s10455-009-9185-5
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DOI: https://doi.org/10.1007/s10455-009-9185-5