Conjugacy in Artin groups and applications to the classification of surfaces

Eddy Godelle; Mina Teicher; Shmuel Kaplan

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arXiv · math/0312188

Conjugacy in Artin groups and applications to the classification of surfaces

Eddy Godelle·Mina Teicher·Shmuel Kaplan

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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.

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Eddy Godelle, Mina Teicher, Shmuel Kaplan. 2003-12-09. Conjugacy in Artin groups and applications to the classification of surfaces. https://arxiv.org/abs/math/0312188

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