2021/08/14 by Chen, Kai-Chieh, McPhail-Snyder, Calvin, Morrison, Scott +1
#FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2108.06561
Kashaev and Reshetikhin previously described a way to define holonomy invariants of knots using quantum \mathfraksl2 at a root of unity. These are generalized quantum invariants depend both on a knot K and a representation of the fundamental group of its complement into SL2(ℂ); equivalently, we can think of KR(K) as associating to each knot a function on (a slight generalization of) its character variety. In this paper we clarify some details of their construction. In particular, we show that for K a hyperbolic knot KaRe(K) can be viewed as a function on the geometric component of the A-polynomial curve of K. We compute some examples at a third root of unity.