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Groups and dynamics -Zlil Sela (HUJI) - Automorphisms of groups and a higher rank JSJ decomposition | Einstein Institute of Mathematics

Groups and dynamics -Zlil Sela (HUJI) - Automorphisms of groups and a higher rank JSJ decomposition

Date: 
Thu, 10/11/202210:00-11:00
Location: 
Ross 70
Title: Automorphisms of groups and a higher rank JSJ decomposition.
Abstract: The JSJ (for groups), that was "borrowed" from 3-manifold
topology, was originally constructed to study the
automorphisms and the cyclic splittings of a (torsion-free) hyperbolic
group. Such a structure theory was needed to complete the solution of the
isomorphism problem for (torsion-free) hyperbolic groups.
Later, the JSJ was generalized to all finitely presented groups. In this
generality it encodes the splittings of a group (in a rather subtle
way), but not all the automorphisms.
We further generalize the JSJ decomposition to study automorphisms of
groups that act on products of hyperbolic spaces, and more generally to
study automorphisms of (some) hierarchically hyperbolic groups (e.g. right
angled Artin groups and special cube complexes). The object that we
construct can be viewed as a higher rank JSJ decomposition,
and can be associated with a general f.p. group.
All the notions will be explained in the talks.