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Regularity and symplectic properties of traceless SU(2) character varieties of tangles

Banff International Research Station for Mathematical Innovation and Discovery

In this talk, we discuss the character variety of traceless fundamental group representations to SU(2) of a tangle complement. Here, traceless means meridians of all n strands are sent to traceless SU(2) elements. There is a restriction map from the traceless character variety of an n-strand tangle to the traceless character variety of the 2n-punctured sphere. We’ll describe the structure of these traceless character varieties and their symplectic properties, and outline a program to define a Lagrangian Floer homology counterpart to Kronheimer Mrowka reduced singular instanton homology, which uses these traceless character varieties. This is joint work with Kirk and Hedden.

Mathematics; Manifolds and cell complexes; Global analysis, analysis on manifolds; Low dimensional topology

video/mp4

Author affiliation: University of Nevada - Reno

2016-09-20

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59219

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/