Real embeddings and eta invariants. (English) Zbl 0795.57010

Bismut, Jean-Michel; Zhang, Weiping

Math. Ann. 295, No. 4, 661-684 (1993).

Let \(i:Y \to X\) be an embedding of real compact odd dimensional manifolds. The purpose of this paper is to establish a formula mod\((\mathbb{Z})\) expressing the difference of certain eta invariants over \(X\) as the sum of an eta invariant over \(Y\) and of integrals over \(X\) and \(Y\) of Chern-Simons currents.

Reviewer: J.-M.Bismut, W.Zhang (Paris)

MSC:

57R20	Characteristic classes and numbers in differential topology
58J20	Index theory and related fixed-point theorems on manifolds
57R40	Embeddings in differential topology

Keywords:

characteristic classes and numbers; index theory and fixed point theory; embedding of real compact odd dimensional manifolds; eta invariants; Chern-Simons currents

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