Holonomy braidings, biquandles and quantum invariants of links with $S{L}_2(\mathbb{C})$ flat connections

Abstract

R. Kashaev and N. Reshetikhin introduced the notion of holonomy braiding extending V. Turaev's homotopy braiding to describe the behavior of cyclic representations of the unrestricted quantum group $U_{q}s{l}_2$ at root of unity. In this paper, using quandles and biquandles we develop a general theory for Reshetikhin-Turaev ribbon type functor for tangles with quandle representations. This theory applies to the unrestricted quantum group $U_{q}s{l}_2$ and produces an invariant of links with a gauge class of quandle representations.

54 pages, 64 figures

References in corpus (2)

• Homology of left non-degenerate set-theoretic solutions to the Yang-Baxter equation
• The trace on projective representations of quantum groups

Cited by in corpus (1)

• Knot quandle decompositions