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

Abstract

Abstract. We study the eta invariants of compact flat spin manifolds of dimension n with holonomy group Zp, 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.We study the eta invariants of compact flat spin manifolds of dimension n with holonomy group Zp, 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.