TY - JOUR
T1 - Automorphisms of groups and a higher rank JSJ decomposition I
T2 - RAAGs and a higher rank Makanin-Razborov diagram
AU - Sela, Z.
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
PY - 2023/6
Y1 - 2023/6
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85159443688&partnerID=8YFLogxK
U2 - 10.1007/s00039-023-00642-x
DO - 10.1007/s00039-023-00642-x
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AN - SCOPUS:85159443688
SN - 1016-443X
VL - 33
SP - 824
EP - 874
JO - Geometric and Functional Analysis
JF - Geometric and Functional Analysis
IS - 3
ER -