Automorphisms of graph products of groups and acylindrical hyperbolicity / Anthony Genevois.

Format:

Book

Author/Creator:

Genevois, Anthony, author.

Series:

Memoirs of the American Mathematical Society ; v. 1509.

Memoirs of the American Mathematical Society, 0065-9266 ; v. 1509

Language:

English

Subjects (All):

Group theory.

Physical Description:

v, 127 pages : illustrations ; 26 cm.

Place of Publication:

Providence : American Mathematical Society, 2024.

Summary:

This article is dedicated to the study of the acylindrical hyperbolicity of automorphism groups of graph products of groups. Our main result is that, if Γ is a finite graph which contains at least two vertices and is not a join and if G is a collection of finitely generated irreducible groups, then either ΓG is infinite dihedral or Aut(ΓG) is acylindrically hyperbolic. This theorem is new even for right-angled Artin groups and right-angled Coxeter groups. Various consequences are deduced from this statement and from the techniques used to prove it. For instance, we show that the automorphism groups of most graph products verify vastness properties such as being SQ-universal; we show that many automorphism groups of graph products do not satisfy Kazhdan's property (T); we solve the isomorphism problem between graph products in some cases; and we show that a graph product of coarse median groups, as defined by Bowditch, is coarse median itself.

Notes:

"September 2024 ; vol. 301 number 1509 (third of 7 numbers)".

Includes bibliographical references (pages 123-126) and index.

ISBN:

1470471396

9781470471392

OCLC:

1467671557