Representations of the Necklace Braid Group: Topological and Combinatorial Approaches
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© 2019, Springer-Verlag GmbH Germany, part of Springer Nature. The necklace braid group NB n is the motion group of the n+ 1 component necklace link L n in Euclidean R 3 . Here L n consists of n pairwise unlinked Euclidean circles each linked to an auxiliary circle. Partially motivated by physical considerations, we study representations of the necklace braid group NB n , especially those obtained as extensions of representations of the braid group B n and the loop braid group LB n . We show that any irreducible B n representation extends to NB n in a standard way. We also find some non-standard extensions of several well-known B n -representations such as the Burau and LKB representations. Moreover, we prove that any local representation of B n (i.e., coming from a braided vector space) can be extended to NB n , in contrast to the situation with LB n . We also discuss some directions for future study from categorical and physical perspectives.
author list (cited authors)
Bullivant, A., Kimball, A., Martin, P., & Rowell, E. C.