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M Sadowski, A Szczepaski

Flat manifolds, harmonic spinors, and eta invariants

Keywords: Spin structure, harmonic spinor, eta invariant, flat manifold

The aim of this paper is to calculate the eta invariants and the dimensions of the spaces of harmonic spinors of an infinite family of closed flat manifolds ℱ_CHD. It consists of some flat manifolds M with cyclic holonomy groups. If M ∈ ℱ_CHD, then we give explicit formulas for η(M) and 𝔥(M). They are expressed in terms of solutions of appropriate congruences in {−1, 1}^k. As an application we investigate the integrability of some &eegr; invariants of ℱ_CHD-manifolds.

Advances in Geometry, Walter de Gruyter

Print ISSN: 1615-715X
Volume: 6, 03/2006
Pages: 287 - 300

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