Some power of an element in a Garside group is conjugate to a periodically geodesic element

Details Some power of an element in a Garside group is conjugate to a periodically geodesic element Some power of an element in a Garside group is conjugate to a periodically geodesic element

2006-04-06

arxiv.org/abs/math/0604144v4

Bulletin of the London Mathematical Society, vol. 40, no. 4, pp. 593-603, 2008

Mathematics

General Topology

Subj-class of this paper should be Geometric Topology; Version published by BLMS

Scientific paper

10.1112/blms/bdn032

We show that for each element $g$ of a Garside group, there exists a positive integer $m$ such that $g^m$ is conjugate to a periodically geodesic element $h$, an element with $|h^n|_\D=|n|\cdot|h|_\D$ for all integers $n$, where $|g|_\D$ denotes the shortest word length of $g$ with respect to the set $\D$ of simple elements. We also show that there is a finite-time algorithm that computes, given an element of a Garside group, its stable super summit set.

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