Related papers: Thompson-like groups, Reidemeister numbers, and fi…

Braided Thompson's groups are finitely presented groups introduced by Brin and Dehornoy which contain the ordinary braid groups $B_n$, the finitary braid group $B_{\infty}$ and Thompson's group $F$ as subgroups. We describe some of the…

We present new results regarding automatic continuity, unifying some diagonalization concepts that have been developed over the years. For example, any homomorphism from a completely metrizable topological group to Thompson's group $F$ has…

Consider the following property of a topological group G: every continuous affine G-action on a Hilbert space with a bounded orbit has a fixed point. We prove that this property characterizes amenability for locally compact sigma-compact…

We introduce a refinement of bounded cohomology and prove that the suitable comparison homomorphisms vanish for an amenable group. We investigate in this context Thompson's group F and provide further evidence towards its amenability. We…

We prove that if F is a finitely generated free group and f:F -> F is an automorphism with polynomial growth of degree d, then there exists a characteristic subgroup S < F of finite index such that the induced automorphism of the…

Consider a proper cocompact CAT(0) space X. We give a complete algebraic characterisation of amenable groups of isometries of X. For amenable discrete subgroups, an even narrower description is derived, implying Q-linearity in the…

The word problem for Thompson's group $F$ has a solution, but it remains unknown whether $F$ is automatic or has a finite or regular convergent (terminating and confluent) rewriting system. We show that the group $F$ admits a natural…

We completely classify fixed point subgroups in Torus Knot Groups, that is groups of the form $G_{p,q} = \langle x , y | x^p = y^q \rangle$. We not only give the isomorphism type, but also the explicit generators for the fixed point…

We give a short and much simplified proof of the main theorem of the recent study, by T. Barthel, M. Hausmann, N. Naumann, T. Nikolaus, J. Noel, and N. Stapleton, of the Balmer spectrum for A-equivariant stable homotopy when A is a finite…

In this article, we study the fixed-point subgroups of the solvable Baumslag-Solitar groups $\BS(1,n)= \langle a, t \mid t a t^{-1} = a^{n} \rangle$, $n>1$ of automorphisms and endomorphisms. We also investigate the stabilizers of subgroups…

We prove that the braided Thompson's groups $V_{\rm br}$ and $F_{\rm br}$ are of type $F_\infty$, confirming a conjecture by John Meier. The proof involves showing that matching complexes of arcs on surfaces are highly connected. In an…

We include a class of generalisations of Thompson's group $V$ introduced by Melanie Stein into the growing framework of topological full groups. Like $V$, Stein's groups can be described as certain piecewise linear maps with prescribed…

The classical result by Dyer--Scott about fixed subgroups of finite order automorphisms of $F_n$ being free factors of $F_n$ is no longer true in $Z^m\times F_n$. Within this more general context, we prove a relaxed version in the spirit of…

A topological group $G$ has the Approximate Fixed Point (AFP) property on a bounded convex subset $C$ of a locally convex space if every continuous affine action of $G$ on $C$ admits a net $(x_i)$, $x_i\in C$, such that…

In this article, we show super-rigidity of Gromov's random monster group. We prove that any morphism $\phi_\alpha$ from Gromov's random monster group $\Gamma_\alpha$ to the group $G$ has finite image for almost all $\alpha$, where $G$ is…

We show how all topological full groups coming from a one-sided irreducible shift of finite type, as studied by Matui, can be re-interpreted as groups of colour-preserving tree almost automorphisms. As an application, we show that they…

We investigate the local topological structure of non-metrizable topological groups through the lens of Tukey order and cofinal types. Motivated by recent advances in topological groups admitting an $\omega^\omega$-base, we introduce the…

Let $\Gamma$ be a discrete group with property $(T)$ of Kazhdan. We prove that any Riemannian isometric action of $\Gamma$ on a compact manifold $X$ is locally rigid. We also prove a more general foliated version of this result. The…

We prove that if $\F$ is an abelian group of $C^1$ diffeomorphisms isotopic to the identity of a closed surface $S$ of genus at least two then there is a common fixed point for all elements of $\F.$

The recent paper "The further chameleon groups of Richard Thompson and Graham Higman: automorphisms via dynamics for the Higman groups $G_{n,r}$" of Bleak, Cameron, Maissel, Navas and Olukoya (BCMNO) characterises the automorphisms of the…