How to read the length of a braid from its curve diagram

Abstract

We prove that the Garside length a braid is equal to a winding-number type invariant of the curve diagram of the braid.

Version 4: Proposition 3.1 of the previous version was wrong. In the current version, a similar statement is made, but only in the form of a conjecture. The main result of the paper is not affected by this mistake

Cited by in corpus (2)

• Reducible braids and Garside theory
• Lawrence-Krammer-Bigelow representations and dual Garside length of braids