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arXiv · 2006.14534

A new proof of the growth rate of the solvable Baumslag-Solitar groups

Jennifer Taback·Alden Walker
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Abstract

We exhibit a regular language of geodesics for a large set of elements of $BS(1,n)$ and show that the growth rate of this language is the growth rate of the group. This provides a straightforward calculation of the growth rate of $BS(1,n)$, which was initially computed by Collins, Edjvet and Gill in [5]. Our methods are based on those we develop in [8] to show that $BS(1,n)$ has a positive density of elements of positive, negative and zero conjugation curvature, as introduced by Bar-Natan, Duchin and Kropholler in [1].

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Jennifer Taback, Alden Walker. 2020-06-25. A new proof of the growth rate of the solvable Baumslag-Solitar groups. https://arxiv.org/abs/2006.14534

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