Kirwan-Novikov inequalities on a manifold with boundary
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- by Maxim Braverman and Valentin Silantyev PDF
- Trans. Amer. Math. Soc. 358 (2006), 3329-3361 Request permission
Abstract:
We extend the Novikov Morse-type inequalities for closed 1-forms in 2 directions. First, we consider manifolds with boundary. Second, we allow a very degenerate structure of the critical set of the form, assuming only that the form is non-degenerated in the sense of Kirwan. In particular, we obtain a generalization of a result of Floer about the usual Morse inequalities on a manifold with boundary. We also obtain an equivariant version of our inequalities. Our proof is based on an application of the Witten deformation technique. The main novelty here is that we consider the neighborhood of the critical set as a manifold with a cylindrical end. This leads to a considerable simplification of the local analysis. In particular, we obtain a new analytic proof of the Morse-Bott inequalities on a closed manifold.References
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Additional Information
- Maxim Braverman
- Affiliation: Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
- MR Author ID: 368038
- Email: maxim@neu.edu
- Valentin Silantyev
- Affiliation: Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
- Email: v.silantyev@neu.edu
- Received by editor(s): April 9, 2004
- Published electronically: February 20, 2006
- Additional Notes: This research was partially supported by NSF grant DMS-0204421
- © Copyright 2006 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 358 (2006), 3329-3361
- MSC (2000): Primary 57R70; Secondary 58A10
- DOI: https://doi.org/10.1090/S0002-9947-06-04021-9
- MathSciNet review: 2218978