Quasi-axis

Description

A Quasi-axis is a quasi-geodesic which is invariant under the a group element. An element with a Quasi-axis is called a Hyperbolic group element.

Definition

Let $G$ be a group acting by isometries on a Hyperbolic metric space $X$. Let $g\in G$. If $g$ fixes a Quasi-geodesic $l$ then the group element is called hyperbolic and $l$ is called a quasi-axis or quasi-geodesic axis.

$g$ acts on $l$ by a positive translation. The direction of positive translation induces an orientation on $l$ called the $g$-orientation. The $g$-orientation is opposite to the $g^{-1}$-orientation.

• I’m strongly suspecting it but is it true that a quasi-geodesic here is a class of quasi-geodesics.

Properties

Examples

Example