### 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 \(SL_2(\mathbb{C})\) 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.)