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Automorphisms of groups and a higher rank JSJ decomposition I: RAAGs and a higher rank Makanin-Razborov diagram

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Abstract

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.

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  1. Hebrew University, 9190401, Jerusalem, Israel

    Z. Sela

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Sela, Z. Automorphisms of groups and a higher rank JSJ decomposition I: RAAGs and a higher rank Makanin-Razborov diagram. Geom. Funct. Anal. 33, 824–874 (2023). https://doi.org/10.1007/s00039-023-00642-x

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