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Automorphisms of Groups and a Higher Rank JSJ Decomposition II: The single ended case

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arxiv 2209.12891 v2 pith:J6IROKDY submitted 2022-09-26 math.GR math.LO

Z. Sela This is my paper · ORCID
classification math.GRmath.LO
keywords automorphismsdecompositionencodesgrouphigherrankgroupshyperbolic
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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 (HHG) that satisfies some weak acylindricity conditions. To study these automorphisms we construct an object that can be viewed as a higher rank JSJ decomposition. This higher rank decomposition encodes the dynamics of individual automorphisms and the structure of the outer automorphism group of an HHG.

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  1. New tools in hierarchical hyperbolicity: A survey

    math.GR 2025-07 accept

    A survey of tools for hierarchical hyperbolicity, including combinatorial HHSs, injective metrics, asymptotically CAT(0) metrics, curtains, R-cubings, and higher-rank JSJ decompositions.

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