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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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.


Flat manifolds Eta invariant Equivariant bordism

Mathematics Subject Classification (2000)