Title: SU(2) Representations of Three-Manifold groups
Speaker: Deeparaj Bhat (MIT)
Date: 28 August 2023
Time: 4:00 pm
Venue: LH-1 (or MS Teams (online) since the author has been keeping unwell)
By the resolution of the Poincare conjecture in 3D, we know that the only closed three-manifold with the trivial fundamental group is the
three-sphere. In light of it, one can ask the following question: Suppose M is a closed three-manifold with the property that the
only representation $\pi_1(M)\rightarrow SU(2)$ is the trivial one. Does this imply that $\pi_1(M)$ is trivial? The class of manifolds $M$ for
which this question is interesting (and open) are integer homology spheres. We prove a result in this direction: the half-Dehn
surgery on any non-trivial fibered knot $K$ in $S^3$ admits an irreducible representation. The proof uses instanton floer homology.
I will give a brief introduction to instanton floer homology and sketch the strategy. This is based on work in progress, some jointly
with Zhenkun Li and Fan Ye.