The University of Sydney - School of Mathematics and Statistics

Thursday 26 March 2015 from 12:00–13:00 in Carslaw 535A

Deformations of the peripherial map for knot complements

Peter Samuelson (Toronto)

Abstract

Deformations of the peripherial map for knot complements Abstract: The space $Rep(M)$ of representations of the fundamental group ${\pi }_1(M)$ of a 3-manifold M into $S{L}_2(\mathbb{C})$ has played an important role in the study of 3-manifolds. If $M=S^3\setminus K$ is the complement of a knot in the 3-sphere, then there is a map $Rep(M)\to Rep(T^2)$ given by restricting representations to the boundary. There is a natural deformation $X(s,t)$ of the space $Rep(T^2)$ depending on two complex parameters which comes from a "double affine Hecke algebra." We will discuss some background and then describe a conjecture that the map $Rep(M)\to Rep(T^2)$ has a canonical deformation to a map $Rep(M)\to X(s,t)$. (This is joint work with Yuri Berest.)