Conjugacy geodesics and growth in dihedral Artin groups

Abstract

In this paper we describe conjugacy geodesic representatives in any dihedral Artin group $G(m)$, $m\ge 3$, which we then use to calculate asymptotics for the conjugacy growth of $G(m)$, and show that the conjugacy growth series of $G(m)$ with respect to the `free product' generating set $\{x,y\}$ is transcendental. We prove two additional properties of $G(m)$ that connect to conjugacy, namely that the permutation conjugator length function is constant, and that the falsification by fellow traveler property (FFTP) holds with respect to $\{x,y\}$. These imply that the language of all conjugacy geodesics in $G(m)$ with respect to $\{x,y\}$ is regular.

Minor edits, to appear in New York Journal of Mathematics

Cited by in corpus (1)

• Twisted conjugacy in dihedral Artin groups I: Torus Knot groups