• Relatively Hyperbolic Extensions of Groups and Cannon-Thurston Maps

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/120/01/0057-0068

• # Keywords

Cannon–Thurston maps; relatively hyperbolic groups.

• # Abstract

Let $1\to(K, K_1)\to(G, N_G(K_1))\to(\mathcal{Q}, \mathcal{Q}_1)\to 1$ be a short exact sequence of pairs of finitely generated groups with $K_1$ a proper non-trivial subgroup of 𝐾 and 𝐾 strongly hyperbolic relative to $K_1$. Assuming that, for all $g\in G$, there exists $k_g\in K$ such that $gK_1g^{-1}=k_gK_1k^{-1}_g$, we will prove that there exists a quasi-isometric section $s:\mathcal{Q}\to G$. Further, we will prove that if 𝐺 is strongly hyperbolic relative to the normalizer subgroup $N_G(K_1)$ and weakly hyperbolic relative to $K_1$, then there exists a Cannon–Thurston map for the inclusion $i:\Gamma_K\to\Gamma_G$.

• # Author Affiliations

1. Stat-Math Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700 108, India

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019