Adiabatic Limits, Nonmultiplicativity of Signature, and Leray Spectral Sequence
نویسندگان
چکیده
منابع مشابه
Adiabatic Limits, Nonmultiplicativity of Signature, and Leray Spectral Sequence
We first prove an adiabatic limit formula for the rf-invariant of aDirac operator, generalizing the recent work of J.-M. Bismut and J. Cheeger.An essential part of the proof is the study of the spectrum of the Dirac op-erator in the adiabatic limit. A new contribution arises in the adiabatic limitformula, in the form of a global term coming from the (asymptotically) verysmal...
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Spectral sequences are a powerful bookkeeping tool, used to handle large amounts of information. As such, they have become nearly ubiquitous in algebraic topology and algebraic geometry. In this paper, we take a few results on faith (i.e., without proof, pointing to books in which proof may be found) in order to streamline and simplify the exposition. From the exact couple formulation of spectr...
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Let (M, F) be a closed foliated manifold, dimM = n, dimF = p, p+q = n, equipped with a Riemannian metric gM . We assume that the foliation F is Riemannian, and the metric gM is bundle-like. Let F = TF be the integrable distribution of tangent p-planes to F , and H = F⊥ be the orthogonal complement to F . The decomposition of TM into a direct sum, TM = F ⊕ H , induces a decomposition of the metr...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 1991
ISSN: 0894-0347
DOI: 10.2307/2939276