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Growth along geodesic rays in hyperbolic groups

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If you have a question about this talk, please contact Simon Baker.

Let G be a non-elementary hyperbolic group equipped with a finite generating set S. Suppose that G acts cocompactly by isometries on a space X. If we fix an origin for X then we can ask the following general question: by how much does a group element g in G displace the origin and, how does this displacement compare to the word length of g (with respect to S)? In this talk we will discuss one way of answering this question. More specifically we will study how the displacement of the origin grows as we travel along infinite geodesic rays in the Cayley graph of G.

This talk is part of the Topology and Dynamics Seminar series.

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