- Series
- Geometry Topology Seminar
- Time
- Monday, November 11, 2013 - 2:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Peter Samuelson – University of Toronto
- Organizer
- Thang Le
Frohman and Gelca showed that the Kauffman bracket skein module of the
thickened torus is the Z_2 invariant subalgebra A'_q of the quantum torus
A_q. This shows that the Kauffman bracket skein module of a knot complement
is a module over A'_q. We discuss a conjecture that this module is
naturally a module over the double affine Hecke algebra H, which is a
3-parameter family of algebras which specializes to A'_q. We give some
evidence for this conjecture and then discuss some corollaries. If time
permits we will also discuss a related topological construction of a
2-parameter family of H-modules associated to a knot in S^3. (All results
in this talk are joint with Yuri Berest.)