Quantum trace and length conjecture for hyperbolic knot

2022-11-11 11:00 - 12:00
CMSA Room G10
Address: CMSA, 20 Garden Street, Cambridge, MA 02138 USA

Member Seminar

Speaker: Mauricio Romo

Title: Quantum trace and length conjecture for hyperbolic knot

Abstract: I will define the quantum trace map for an ideally triangulated hyperbolic knot complement on S^3. This map assigns an operator to each element L of  the Kauffman Skein module of knot complement.  Motivated by an interpretation of this operator in the context of SL(2,C) Chern-Simons theory, one can formulate a ‘length conjecture’ for the hyperbolic length of L.