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Induced Cyclic Cocycles and Higher Eta Invariants

✍ Scribed by Ronald G. Douglas; Jerome Kaminker

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 433 KB
Volume: 147
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1996.3049

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✦ Synopsis

We construct some cyclic cocycles on the foliation algebra and show that the result of pairing them with a leafwise Dirac operator is a spectral invariant. This leads to a notation of higher eta invariants.

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Let Σ be a 3-dimensional oriented manifold and let K ⊂ Σ be a knot. We assume that Σ is an integer homology sphere and (Σ, K) has a plumbing representation. We denote the cyclic n-fold covering of Σ branched along K by Σ(K, n), and we assume that this manifold is integer homology sphere as well. If