Dawid Kielak

Outer automorphism groups of free groups: linear and free representations

We study the existence of homomorphisms between Out(F_n) and Out(F_m) for n > 5 and m < n(n-1)/2, and conclude that if m is not equal to n then each such homomorphism factors through the finite group of order 2. In particular this provides an answer to a question of Bogopolskii and Puga. In the course of the argument linear representations of Out(F_n) in dimension less than n(n+1)/2 over fields of characteristic zero are completely classified. It is shown that each such representation has to factor through the natural projection from Out(F_n) to GL(n,Z) coming from the action of Out(F_n) on the abelianisation of F_n. We obtain similar results about linear representation theory of Out(F_4) and Out(F_5).

Alexander and Thurston norms, and the Bieri–Neumann–Strebel invariants for free-by-cyclic groups

We investigate Friedl-Lucks universal

Nielsen realisation for untwisted automorphisms of right‐angled Artin groups

L^2

Outer actions of Out(Fn) on small right-angled Artin groups

-torsion for descending HNN extensions of finitely generated free groups, and so in particular for

Groups with infinitely many ends are not fraction groups

F_n

The 6-strand braid group is CAT(0)

-by-

The Bieri-Neumann-Strebel invariants via Newton polytopes

\mathbb{Z}

Free and linear representations of outer automorphism groups of free groups

groups. This invariant induces a semi-norm on the first cohomology of the group which is an analogue of the Thurston norm for

Nielsen Realization by Gluing: Limit Groups and Free Products

3

On the smallest non-abelian quotient of

-manifold groups. We prove that this Thurston semi-norm is an upper bound for the Alexander semi-norm defined by McMullen, as well as for the higher Alexander semi-norms defined by Harvey. The same inequalities are known to hold for