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. Gilkey
  • Roberto J. Miatello
  • Ricardo A. Podestá

DOI: 10.1007/s10455-009-9185-5

Cite this article as:
Gilkey, P.B., Miatello, R.J. & Podestá, R.A. Ann Glob Anal Geom (2010) 37: 275. doi:10.1007/s10455-009-9185-5


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)


Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Peter B. Gilkey
    • 1
  • Roberto J. Miatello
    • 2
  • Ricardo A. Podestá
    • 2
  1. 1.Mathematics DepartmentUniversity of OregonEugeneUSA
  2. 2.FaMAF – CIEM, Universidad Nacional de CórdobaCórdobaArgentina

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