Eta series and eta invariants of Z4-manifolds

RICARDO A. PODESTÁ

REVISTA DE LA UNIóN MATEMáTICA ARGENTINA

Unión Matemática Argentina

Año: 2005 vol. 46 p. 31 - 45

0041-6932

In this paper, for each n=4r+3, we construct a family of compact flat spin n-manifolds with holonomy group isomorphic to Z4 such that the spectrum of the Dirac operator D is asymmetric. For these manifolds we will obtain explicit expressions for the eta series, eta(s), in termsof Hurwitz zeta functions, and for the eta-invariant, eta(0), associated to D. The explicit expressions will show the meromorphic continuation of eta(s) to the complex plane C is in fact everywhere holomorphic.