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

Eon-Kyung Lee·Sang-Jin Lee
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Abstract

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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Eon-Kyung Lee, Sang-Jin Lee. 2009-06-18. Some power of an element in a Garside group is conjugate to a periodically geodesic element. https://doi.org/10.1112/blms%2Fbdn032

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