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Novikov type inequalities for differential forms with non-isolated zeros

Published online by Cambridge University Press:  01 September 1997

MAXIM BRAVERMAN
Affiliation:
School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv 69978, Israel; e-mail: maxim@math.tau.ac.il, farber@math.tau.ac.il
MICHAEL FARBER
Affiliation:
School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv 69978, Israel; e-mail: maxim@math.tau.ac.il, farber@math.tau.ac.il

Abstract

We generalize the Novikov inequalities for 1-forms in two different directions: first, we allow non-isolated critical points (assuming that they are non-degenerate in the sense of R. Bott) and, secondly, we strengthen the inequalities by means of twisting by an arbitrary flat bundle. The proof uses Bismut's modification of the Witten deformation of the de Rham complex; it is based on an explicit estimate on the lower part of the spectrum of the corresponding Laplacian.

In particular, we obtain a new analytic proof of the degenerate Morse inequalities of Bott.

Type
Research Article
Copyright
Cambridge Philosophical Society 1997

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