TY - JOUR

T1 - Novikov type inequalities for differential forms with non-isolated zeros

AU - Braverman, Maxim

AU - Farber, Michael

PY - 1997/9

Y1 - 1997/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33746811062&partnerID=8YFLogxK

U2 - 10.1017/S0305004197001734

DO - 10.1017/S0305004197001734

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AN - SCOPUS:33746811062

SN - 0305-0041

VL - 122

SP - 357

EP - 375

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

IS - 2

ER -