Novikov type inequalities for differential forms with non-isolated zeros

Details Novikov type inequalities for differential forms with non-isolated zeros Novikov type inequalities for differential forms with non-isolated zeros

1995-08-14

arxiv.org/abs/dg-ga/9508006v1

Mathematics

Differential Geometry

23 pages; AMS-LaTeX

Scientific paper

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.

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