Eta invariant and equivariant bordism of flat manifolds

RICARDO A. PODESTÁ

Schloss Rauischholzhausen, Marburg, Alemania

Congreso; Dirac operators and special geometries; 2009

Phillips UNiversitat Marburg

In this joint work with Peter Gilkey and Roberto Miatello we study the eta invariants of compact flat spin manifolds of odd dimension n with holonomy group Zp, where p is an odd prime, for twisted Dirac operators.We find explicit expressions for the twisted and relative eta invariants and show that the eta invariant is always an integer, except in a single case. We use the expressions obtained to show that any such manifold is trivial in the appropriate reduced equivariant spin bordism group.