Holonomy Braidings, Biquandles and Quantum Invariants of Links with SL2(C) Flat Connections

Authors

Christian Blanchet, Universite de Paris
Alexandra Tebbs, Utah State University
Bertrand Patureau-Mirand, Universite de Bretagne Sud
Nicolai Reshetikhin, University of California - Berkeley

Document Type

Article

Journal/Book Title/Conference

Selecta Mathematica

Volume

26

Publisher

Birkhaeuser Science

Publication Date

3-3-2020

Award Number

NSF, Division of Mathematical Sciences 1664387

Funder

NSF, Division of Mathematical Sciences

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_qsl(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_qsl(2) and produces an invariant of links with a gauge class of quandle representations.

Recommended Citation

Blanchet, C., Geer, N., Patureau-Mirand, B., & Reshetikhin, N. (2020). “Holonomy Braidings, Biquandles and Quantum Invariants of Links with SL2(C) Flat Connections.” Selecta Mathematica, vol. 26, no. 2, p. 19. https://doi.org/10.1007/s00029-020-0545-0