Symplectic Morse theory and Witten deformation
Abstract
Abstract 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 results from 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.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Geometry and complex manifolds
Geometric and Algebraic Topology
Publication details
- Journal / source
- Mathematische Zeitschrift
- Publisher
- Springer Science and Business Media LLC
- Volume
- 312
- Issue
- 3
- Publication date
- 1 March 2026
- Language
- EN