Novikov type inequalities for differential forms with non-isolated zeros

Maxim Braverman*, Michael Farber

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)357-375
Number of pages19
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number2
StatePublished - Sep 1997


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