University of Cambridge > Talks.cam > Differential Geometry and Topology Seminar > Holonomy perturbations and irreducible SL(2,C)-representations of homology 3-spheres

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

Add to your list(s) Download to your calendar using vCal

  • UserRaphael Zentner, Regensburg
  • ClockWednesday 19 October 2016, 16:00-17:00
  • HouseMR13.

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.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2022 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity