Mathematical Proceedings of the Cambridge Philosophical Society


Research Article

Novikov type inequalities for differential forms with non-isolated zeros


MAXIM BRAVERMAN a1 and MICHAEL FARBER a1
a1 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.

(Received August 17 1995)