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The Novikov-Bott inequalities

Maxim Braverman·Michael Farber
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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. We also obtain an $L^2$ version of these inequalities with finite von Neumann algebras. The proof of the main theorem 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.

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Maxim Braverman, Michael Farber. 1995-08-16. The Novikov-Bott inequalities. https://arxiv.org/abs/dg-ga/9508009

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