Abstract
We study the local linear representations of the braid group B 3 and the homogeneous local representations of B n for n ≥ 2. We investigate the connection of these representations with the Burau representation. The linear representations of B n are constructed from the Wada representation of B n in the automorphism group of a free group.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Birman J. S., Braids, Links and Mapping Class Groups, Princeton Univ. Press, Princeton (1975).
Kassel C. and Turaev V., Braid Groups, Springer Science+Business Media, New York (2008) (Grad. Texts Math.; V. 247).
Wada M., “Group invariants of links,” Topology, 31, 399–406 (1992).
Shpilrain V., “Representing braids by automorphisms,” Int. J. Algebra Comput., 11, No. 6, 773–777 (2001).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text Copyright © 2013 Mikhalchishina Yu.A.
__________
Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 4, pp. 838–851, July–August, 2013.
Rights and permissions
About this article
Cite this article
Mikhalchishina, Y.A. Local representations of braid groups. Sib Math J 54, 666–678 (2013). https://doi.org/10.1134/S0037446613040083
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0037446613040083