1995/08/14 by Maxim Braverman, Michael Färber, Braverman, Maxim +1 · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.dg-ga/9508006
openalex publication_date 1995/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.