2022/01/17 by Z. Sela, Sela, Z.
Chemistry · Mathematics · Physics and Astronomy · #Carbohydrate Chemistry and Synthesis #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Logic (math.LO) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2201.06320
openalex publication_date 2022/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
The JSJ decomposition encodes the automorphisms and the virtually cyclic splittings of a hyperbolic group. For general finitely presented groups, the JSJ decomposition encodes only their splittings. In this sequence of papers we study the automorphisms of a hierarchically hyperbolic group that satisfies some weak acylindricity conditions. To study these automorphisms we construct an object that can be viewed as a higher rank JSJ decomposition. In the first paper we demonstrate our construction in the case of a right angled Artin group. For studying automorphisms of a general HHG we construct what we view as a higher rank Makanin-Razborov diagram, which is the first step in the construction of the higher rank JSJ.