×

Real embeddings, \(\eta\)-invariant and Chern-Simons current. (English) Zbl 1185.58009

The paper under review is a continuation of a remarkable paper by W. Zhang [Chin. Ann. Math., Ser. B 26, No. 1, 45–56 (2005; Zbl 1078.58012)], where the author has given a geometric proof of the Bismut-Zhang formula. In this paper, the authors apply the method given in the above paper to manifolds embedded in sufficiently high dimensional odd spheres \(S^{2N-1}\). They also establish a Riemann-Roch-type formula for the considered Chern-Simons currents.

MSC:

58J28 Eta-invariants, Chern-Simons invariants

Citations:

Zbl 1078.58012
PDFBibTeX XMLCite
Full Text: DOI arXiv