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1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

Abstract : A result by Dehornoy 1992 says that every nontrivial braid admits a sigma-definite word representative, defined as a braid word in which the generator sigma i with maximal index i appears with exponents that are all positive, or all negative. This is the ground result for ordering braids. In this paper, we enhance this result and prove that every braid admits a sigma-definite word representative that, in addition, is quasi-geodesic. This establishes a longstanding conjecture. Our proof uses the dual braid monoid and a new normal form called the rotating normal form.

Keywords : braid ordering braid monoid dual braid monoid sigma-definite representative

Author: Jean Fromentin -

Source: https://hal.archives-ouvertes.fr/


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