Topology Seminar (Main Talk): Irreducible $SL(2,\mathbb C)$-representations of integer homology 3-spheres

Seminar | December 6 | 4-5 p.m. | 3 Evans Hall

 Raphael Zentner, University of Regensburg

 Department of Mathematics

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 $SL(2,\mathbb C)$.