Swathi Krishna
TIFR, Mumbai
October 13, 2022
Existence of Cannon-Thurston map: Let $G$ be a hyperbolic group and $H$ be a hyperbolic subgroup of $G$. If the embedding $H\to G$ extends continuously to a map between the Gromov compactifications of the groups, this extension is called a Cannon-Thurston map (CT). While it is known that not every hyperbolic subgroup embedding in a hyperbolic group admits CT, over time the existence of CT has been proven in many cases. We will start with a survey of these results and move on to the following case where CT exists. Let $1 \to N \to G \stackrel{\pi}{\to} Q \to 1$ be a short exact sequence of non-elementary hyperbolic groups and $K=\pi^{-1}(Q_1)$, where $Q_1$ is a qi-embedded subgroup of $Q$. Then $K$ is hyperbolic and $K \to G$ admits CT. This is part of joint work with Pranab Sardar.
TIFR, Mumbai
October 13, 2022
Existence of Cannon-Thurston map: Let $G$ be a hyperbolic group and $H$ be a hyperbolic subgroup of $G$. If the embedding $H\to G$ extends continuously to a map between the Gromov compactifications of the groups, this extension is called a Cannon-Thurston map (CT). While it is known that not every hyperbolic subgroup embedding in a hyperbolic group admits CT, over time the existence of CT has been proven in many cases. We will start with a survey of these results and move on to the following case where CT exists. Let $1 \to N \to G \stackrel{\pi}{\to} Q \to 1$ be a short exact sequence of non-elementary hyperbolic groups and $K=\pi^{-1}(Q_1)$, where $Q_1$ is a qi-embedded subgroup of $Q$. Then $K$ is hyperbolic and $K \to G$ admits CT. This is part of joint work with Pranab Sardar.