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 manifoldsEta invariantEquivariant 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