The Novikov-Bott inequalities
dg-ga
2016-08-31 v1 Differential Geometry
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 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.
Keywords
Cite
@article{arxiv.dg-ga/9508009,
title = {The Novikov-Bott inequalities},
author = {Maxim Braverman and Michael Farber},
journal= {arXiv preprint arXiv:dg-ga/9508009},
year = {2016}
}
Comments
6 pages; AMS-LaTeX. We give a short review of the results of dg-ga/9508006. We also present an L^2 generalization of these results