Biracks and switch braid quivers (Q6635479)

The authors of this article introduce a new family of braid group representations derived from switch colorings, called switch braid representations. These representations are precisely the permutation representations from [\textit{R. Fenn} et al., Topology Appl. 145, No. 1--3, 157--175 (2004; Zbl 1063.57006)] which restrict to representations in the category of switches. The authors also introduce a finite quiver-valued invariant of braids using finite biracks and switches. Furthermore, they enhance the switch braid quiver invariants with birack cocycles and obtain two new families of 2-variable polynomial invariants of braids as decategorifications of the birack braid cocycle quiver.