2020/06/25 by Jennifer Taback, Taback, Jennifer, Alden Walker +1
Mathematics · #20F65 (Primary) 20F10 #26A12 (Secondary) #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.2006.14534
openalex publication_date 2020/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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].