# Zabrodsky Lecture 1 (Colloquium): Kenji Fukaya (SCGP) - Instanton Floer homology for 3 manifold with boundary

Date:
Thu, 24/03/202214:30-15:30
Location:
Lecture hall 2, Manchester building
Lecturer:
Kenji Fukaya (Simons Center for Geometry and Physics)
Title: Instanton Floer homology for 3 manifold with boundary

Abstract: In this talk I will explain an ongoing joint work with A. Daemi (and partially with M. Lipyanskiy) to build topological Field theory of dimension 2-3-4 based on Donaldson-Floer theory (Yang-Mills or ASD equation). The part which is completed so far is based on SO(3) bundle with nontrivial Stiefel-Whitney class, (to avoid a singularity of the moduli space). In such a case we can construct a topological field theory (some part is to be written). This problem is related to a conjecture by Atiyah and Floer which relate Instanton Floer homology (Gauge theory) to Lagrangian Floer theory (Symplectic geometry).