Article

Annals of Global Analysis and Geometry

, Volume 37, Issue 3, pp 275-306

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

  • Peter B. GilkeyAffiliated withMathematics Department, University of Oregon
  • , Roberto J. MiatelloAffiliated withFaMAF – CIEM, Universidad Nacional de Córdoba Email author 
  • , Ricardo A. PodestáAffiliated withFaMAF – CIEM, Universidad Nacional de Córdoba

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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.

Keywords

Flat manifolds Eta invariant Equivariant bordism

Mathematics Subject Classification (2000)

58J53