Automorphisms of Groups and a Higher Rank JSJ Decomposition I: RAAGs and a Higher Rank Makanin-Razborov Diagram

Z. Sela

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arXiv · 2201.06320

Automorphisms of Groups and a Higher Rank JSJ Decomposition I: RAAGs and a Higher Rank Makanin-Razborov Diagram

Z. Sela

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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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Z. Sela. 2022-01-17. Automorphisms of Groups and a Higher Rank JSJ Decomposition I: RAAGs and a Higher Rank Makanin-Razborov Diagram. https://arxiv.org/abs/2201.06320

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