Dependence on the spin structure of the eta and rokhlin invariants

Details Dependence on the spin structure of the eta and rokhlin invariants Dependence on the spin structure of the eta and rokhlin invariants

1999-12-21

arxiv.org/abs/math/9912168v1

Topology Appl. 118 (2002), no. 3, 345-355

Mathematics

Differential Geometry

10 pages

Scientific paper

10.1016/S0166-8641(01)00033-5

We study the dependence of the eta invariant $\eta_D$ on the spin structure, where $D$ is a twisted Dirac operator on a (4k+3)-dimensional spin manifold. The difference between the eta invariants for two spin structures related by a cohomolgy class which is the reduction of a $H^1(M,\Za)$-class is shown to be a half integer. As an application of the technique of proof the generalized Rokhlin invariant is shown to be equal modulo 8 for two spin structures related in this way.

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