Seminars & Colloquia Calendar
Irreducible SL(2,C)-representations of integer homology 3-spheres
Raphael Zentner -- University of Regensburg, Germany
Location: Hill 705
Date & time: Tuesday, 04 December 2018 at 3:00PM - 4:00PM
Abstract: 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).