Irreducible SL(2,C)-representations of homology-3-spheres
SEMINARS: GAUGE THEORY AND TOPOLOGY, SEMINARS: SYMPLECTIC GEOMETRY
When: December 7, 2018
3:30 pm - 4:30 pm
Where: Science Center 507
Address:
1 Oxford Street, Cambridge, MA 02138, United States
Speaker: Raphael Zentner - Regensburg
We prove that the splicing of any two non-trivial knots in the 3-sphere admits an irreducible SU(2)-representation of its fundamental group. This uses instanton gauge theory, and in particular a non-vanishing result of Kronheimer-Mrowka and some new results that we establish for holonomy perturbations of the ASD equation. Using a result of Boileau, Rubinstein, and Wang (which builds on the geometrization theorem of 3-manifolds), it follows that the fundamental group of any integer homology 3-sphere different from the 3-sphere admits irreducible representations of its fundamental group in SL(2,C).