Gauge Theory Seminar: "3-manifold representations and Rokhlin invariant"

Abstract: Fundamental group provides an important topological invariant of 3-manifolds. For instance, Poincare conjecture asserts that any 3-manifold with the trivial fundamental group is homeomorphic to the 3-dimensional sphere. This motivates the following question: When does the fundamental group of a 3-manifold admit a non-trivial representation into a given Lie group G? In this expository talk, I will explain how one can get a positive answer to this question for ''half'' of all 3-manifolds. Along the way, I highlight a few ideas which are influential in the development of various versions of Floer homologies.