Holonomy braidings, biquandles and quantum invariants of links with SL2(C) flat connections

Christian Blanchet ^[3] ; Nathan Geer ^[1] ; Bertrand Patureau-Mirand ^[4] ; Nicolai Reshetikhin ^[2]
1. [1] Utah State University
  
  Utah State University
  
  Estados Unidos
2. [2] University of California System
  
  University of California System
  
  Estados Unidos
3. [3] Université de Paris, Sorbonne Université, Francia
4. [4] Université de Bretagne-Sud, Francia
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Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 2, 2020
Idioma: inglés
DOI: 10.1007/s00029-020-0545-0
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Resumen
- 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 Uqsl(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 Uqsl(2) and produces an invariant of links with a gauge class of quandle representations.