η-invariant and Chern-Simons current
نویسنده
چکیده
We show that the R/Z part of the analytically defined η invariant of Atiyah-PatodiSinger for a Dirac operator on an odd dimensional closed spin manifold can be expressed purely geometrically through a stable Chern-Simons current on a higher dimensional sphere. As a preliminary application, we discuss the relation with the Atiyah-PatodiSinger R/Z index theorem for unitary flat vector bundles, and prove an R refinement in the case where the Dirac operator is replaced by the Signature operator. We also extend the above discussion to the case of η invariants associated to Hermitian vector bundles with non-unitary connection, which are constructed by using a trick due to Lott.
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