Geodesics in the Braid Group on Three Strands
نویسنده
چکیده
We study the geodesic growth series of the braid group on three strands, B3 := 〈a, b|aba = bab〉. We show that the set of geodesics of B3 with respect to the generating set S := {a, b} ±1 is a regular language, and we provide an explicit computation of the geodesic growth series with respect to this set of generators. In the process, we give a necessary and sufficient condition for a freely reduced word w ∈ S to be geodesic in B3 with respect to S. Also, we show that the translation length with respect to S of any element in B3 is an integer.
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