Symplectic Morse Theory and Witten Deformation
| Autor: | Clausen, David, Tang, Xiang, Tseng, Li-Sheng |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | On symplectic manifolds, we introduce a Morse-type complex with elements generated by pairs of critical points of a Morse function. The differential of the complex consists of gradient flows and an integration of the symplectic structure over spaces of gradient flow lines. Using the Witten deformation method, we prove that the cohomology of this complex is independent of both the Riemannian metric and the Morse function used to define the complex and is in fact isomorphic to the cohomology of differential forms of Tsai, Tseng and Yau (TTY). We also obtain Morse-type inequalities that bound the dimensions of the TTY cohomologies by the number of Morse critical points and the interaction of symplectic structure with the critical points. Comment: v1: 27 pages, 1 figure. v2: 53 pages. Significant changes including title and abstract. The original v1 paper has been greatly expanded and now separated into two papers. One of the two is this replaced version which concerns the symplectic case and uses analytic-based methods. v3: Minor revisions, typos corrected |
| Databáze: | arXiv |
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