Topology Seminar

Date: November 17, 2021

Time: 4:00PM - 5:00PM

Location: Zoom

Speaker: Erkao Bao, University of Minnesota

Title: An invitation to contact homology

Abstract: Contact homology is an invariant of the contact structure, which is an odd-dimensional counterpart of a symplectic structure. It was proposed by Eliashberg, Givental and Hofer in 2000. The application of contact homology and its variants include distinguishing contact structures, knot invariants, the Weinstein conjecture and generalization, and calculating Gromov-Witten invariants. In this talk, I will start with the notion of contact structures, then give a heuristic definition of the contact homology as an infinite dimensional Morse homology, and explain the major difficulties to make the definition rigorous. In the very end, I will talk about the chain homotopy type of contact differential graded algebra. This is a joint work with Ko Honda.