Holonomy perturbations and irreducible SL(2,C)-representations of homology 3-spheres

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• Raphael Zentner, Regensburg
• Wednesday 19 October 2016, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Ivan Smith.

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. Using a result of Boileau, Rubinstein and Wang, 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). Our result uses instanton gauge theory. The essential new input we establish is the following: Any area-preserving isotopy of the SU(2)-representation variety of the 2-torus can be C^0-approximated by maps which are realised geometrically through holonomy perturbations of the flatness equation in a thickened torus.

This talk is part of the Differential Geometry and Topology Seminar series.

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