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arXiv · 1212.6611

Growth of quotients of groups acting by isometries on Gromov hyperbolic spaces

Stephane Sabourau
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Abstract

We show that every non-elementary group $G$ acting properly and cocompactly by isometries on a proper geodesic Gromov hyperbolic space $X$ is growth tight. In other words, the exponential growth rate of $G$ for the geometric (pseudo)-distance induced by $X$ is greater than the exponential growth rate of any of its quotients by an infinite normal subgroup. This result generalizes from a unified framework previous works of Arzhantseva-Lysenok and Sambusetti, and provides an answer to a question of the latter.

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Stephane Sabourau. 2012-12-29. Growth of quotients of groups acting by isometries on Gromov hyperbolic spaces. https://arxiv.org/abs/1212.6611

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