Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: SU(2) Representations of Three-Manifold groups
Speaker: Deeparaj Bhat, MIT
Date: July 31, 2023
Time: 16:00:00 Hours
Venue: A-369
Abstract: By the resolution of the Poincare conjecture in 3D, we know that the only closed three-manifold with 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) --> 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 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 proof. This is based on work in progress, some jointly with Zhenkun Li and Fan Ye.
Title of Talk: SU(2) Representations of Three-Manifold groups
Speaker: Deeparaj Bhat, MIT
Date: July 31, 2023
Time: 16:00:00 Hours
Venue: A-369
Abstract: By the resolution of the Poincare conjecture in 3D, we know that the only closed three-manifold with 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) --> 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 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 proof. This is based on work in progress, some jointly with Zhenkun Li and Fan Ye.