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

Z. Sela*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageAmerican English
Pages (from-to)824-874
Number of pages51
JournalGeometric and Functional Analysis
Volume33
Issue number3
DOIs
StatePublished - Jun 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Fingerprint

Dive into the research topics of 'Automorphisms of groups and a higher rank JSJ decomposition I: RAAGs and a higher rank Makanin-Razborov diagram'. Together they form a unique fingerprint.

Cite this