Conjugacy in Artin groups and applications to the classification of surfaces

2003/12/09 by Eddy Godelle, Godelle, Eddy, Mina Teicher +3
Mathematics · #14J10 #20F36 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:14J10 #msc:20F36

paper · pdf · doi:10.48550/arxiv.math/0312188

arxiv created 2003/12/09 · arxiv updated 2009/12/01

Abstract

We show thatthe double reversing algorithm proposed by dehornoy for solving the word problem in the braid group can also be used to recognize the conjugates of powers of the generators in an Artin group of spherical type. The proof uses a characterization of these powers in terms of their fractional decomposition. This algorithm could have potential applications to braid-based cryptography; it also provides a fast method for testing a necessary condition in the classification of surfaces in algebraic geometry.

Related

• Identifying Powers of Half-Twists and Computing its Root
• Conjugacy problem for braid groups and Garside groups
• On the cycling operation in braid groups
• Conjugacy in Artin groups of extra-large type
• Implementation: The conjugacy problem in right-angled Artin groups