3rd Year Candidacy Presentation: Morse Cohomology and Its Mapping Cone

Abstract: Motivated by the mapping cone construction in homological algebra, in this talk, we will introduce a cone complex for Morse theory on a compact manifold associated with a closed form \psi. Analogous to the Morse cohomology, the cone Morse cohomology is a topological invariant, independent of the choice of the Morse-Smale pair in its definition. We will explain the application of this construction to a symplectic manifold (M, \omega), in which interesting new information was found. If time permits, we will propose some questions for future investigations.

Advisor: Prof. Xiang Tang