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Dependence on the spin structure of the eta and rokhlin invariants

Mattias Dahl
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Abstract

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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Mattias Dahl. 1999-12-21. Dependence on the spin structure of the eta and rokhlin invariants. https://doi.org/10.1016/s0166-8641(01)00033-5

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