Swiss Knots 2011

Knot Theory and Algebra

Lake Thun, May 23-27

Monoidal categories and invariants of links in 3-manifolds

Prof. Dr. Rinat Kashaev's talk
Date: 26.05.11   Time: 09.00 - 09.50   Room: Gwatt Zentrum

Coauthors: Nathan Geer, Vladimir Turaev

Abstract: I will describe a construction of a particular class of state-sum invariants of links in arbitrary compact closed 3-manifolds, where the underlying algebraic input is given by a specific system (called Psi-system) of simple objects of a linear monoidal category, while the underlying combinatorial framework is given by Hamiltonian triangulations, i.e. triangulations where the link is realized as a 1-dimensional subcomplex containing all the vertices (Hamiltonian path in graph theoretical terms). The basic example of this construction is the quantum dilogarithmic link invariant in 3-manifolds which in the case of 3-sphere coincides with the special value of the colored Jones polynomial entering the hyperbolic volume conjecture.