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SUMMARY:Holonomy perturbations and irreducible SL(2\,C)-representations of
  homology 3-spheres - Raphael Zentner\, Regensburg
DTSTART:20161019T150000Z
DTEND:20161019T160000Z
UID:TALK66472@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:We prove that the splicing of any two non-trivial knots in the
  3-sphere admits an irreducible SU(2)-representation of its fundamental gr
 oup.\nUsing a result of Boileau\, Rubinstein and Wang\, it follows that th
 e fundamental group of any integer homology 3-sphere different from the 3-
 sphere admits irreducible representations of its fundamental group in SL(2
 \,C).\n Our result uses instanton gauge theory. The essential new input we
  establish is the following: Any area-preserving isotopy of the SU(2)-repr
 esentation variety of the 2-torus can be C^0-approximated by maps which ar
 e realised geometrically through holonomy perturbations of the flatness eq
 uation in a thickened torus.
LOCATION:MR13
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