Equivariant cohomology is adapted from ordinary cohomology to better capture the action of a group on a topological space. In Floer theory, given an autonomous Hamiltonian, there is a natural action of the circle on 1-periodic flowlines given by time translation. Combining these two ideas leads to the definition of $S^1$-equivariant symplectic cohomology. In this talk, I will introduce these ideas and explain how they are related. I will not assume prior knowledge of Floer theory.
- Junior Geometry and Topology Seminar