Geometry & Topology
- Geom. Topol.
- Volume 19, Number 3 (2015), 1361-1381.
Lawrence–Krammer–Bigelow representations and dual Garside length of braids
We show that the span of the variable in the Lawrence–Krammer–Bigelow representation matrix of a braid is equal to twice the dual Garside length of the braid, as was conjectured by Krammer. Our proof is close in spirit to Bigelow’s geometric approach. The key observation is that the dual Garside length of a braid can be read off a certain labeling of its curve diagram.
Geom. Topol., Volume 19, Number 3 (2015), 1361-1381.
Received: 13 December 2013
Accepted: 26 August 2014
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20F36: Braid groups; Artin groups
Secondary: 20F10: Word problems, other decision problems, connections with logic and automata [See also 03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70] 57M07: Topological methods in group theory
Ito, Tetsuya; Wiest, Bertold. Lawrence–Krammer–Bigelow representations and dual Garside length of braids. Geom. Topol. 19 (2015), no. 3, 1361--1381. doi:10.2140/gt.2015.19.1361. https://projecteuclid.org/euclid.gt/1510858764