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2015 Lawrence–Krammer–Bigelow representations and dual Garside length of braids
Tetsuya Ito, Bertold Wiest
Geom. Topol. 19(3): 1361-1381 (2015). DOI: 10.2140/gt.2015.19.1361

Abstract

We show that the span of the variable q 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.

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Tetsuya Ito. Bertold Wiest. "Lawrence–Krammer–Bigelow representations and dual Garside length of braids." Geom. Topol. 19 (3) 1361 - 1381, 2015. https://doi.org/10.2140/gt.2015.19.1361

Information

Received: 13 December 2013; Accepted: 26 August 2014; Published: 2015
First available in Project Euclid: 16 November 2017

zbMATH: 1345.20049
MathSciNet: MR3352238
Digital Object Identifier: 10.2140/gt.2015.19.1361

Subjects:
Primary: 20F36
Secondary: 20F10, 57M07

Rights: Copyright © 2015 Mathematical Sciences Publishers

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Vol.19 • No. 3 • 2015
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