Related papers: Topological Quasi-Group Shifts

We prove two results. (1) There is an absolute constant $D$ such that for any finite quasisimple group $S$, given 2D arbitrary automorphisms of $S$, every element of $S$ is equal to a product of $D$ `twisted commutators' defined by the…

We survey recent results on multiple transitivity of automorphism groups of affine algebraic varieties. We consider the property of infinite transitivity of the special automorphism group, which is equivalent to flexibility of the…

We conjecture that the automorphism group of a topological parallelism on real projective 3-space is compact. We prove that at least the identity component of this group is, indeed, compact.

We study the class $HQ(\mathbb{D})$, the set of harmonic quasiconformal automorphisms of the unit disk $\mathbb{D}$ in the complex plane, endowed with the topology of uniform convergence. Several important topological properties of this…

Given a group acting cellularly and cocompactly on a simply-connected 2-complex, we provide a criterion establishing that all finitely generated subgroups have quasiconvex orbits. This work generalizes the "perimeter method". As an…

We show that an automorphism of an arbitrary CAT(0) cube complex either has a fixed point or preserves some combinatorial axis. It follows that when a group contains a distorted cyclic subgroup, it admits no proper action on a discrete…

Let $(X,G)$ be a minimal equicontinuous dynamical system, where $X$ is a compact metric space and $G$ some topological group acting on $X$. Under very mild assumptions, we show that the class of regular almost automorphic extensions of…

We show that the automorphism group of a certain subclass of smooth Gizatullin surfaces with a distinguished and rigid extended divisor is generated by automorphisms of A1-fibrations. Moreover, such surfaces provide examples of smooth…

In this article we study the automorphism group ${\rm Aut}(X,\sigma)$ of subshifts $(X,\sigma)$ of low word complexity. In particular, we prove that Aut$(X,\sigma)$ is virtually $\mathbb{Z}$ for aperiodic minimal subshifts and certain…

It is shown that the Cuntz semigroup of a space with dimension at most two, and with second cohomology of its compact subsets equal to zero, is isomorphic to the ordered semigroup of lower semicontinuous functions on the space with values…

We discuss $C^0$-continuous homogeneous quasi-morphisms on the identity component of the group of compactly supported symplectomorphisms of a symplectic manifold. Such quasi-morphisms extend to the $C^0$-closure of this group inside the…

The purpose of this note is twofold. In the first part we observe that two finitely generated non-amenable groups are quasi-isometric if and only if they admit topologically orbit equivalent Cantor minimal actions. In particular, free…

The main goal of this note is to suggest an algebraic approach to the quasi-isometric classification of partially commutative groups (alias right-angled Artin groups). More precisely, we conjecture that if the partially commutative groups…

We prove several results concerning automorphism groups of quasismooth complex weighted projective hypersurfaces; these generalize and strengthen existing results for hypersurfaces in ordinary projective space. First, we prove in most cases…

We prove that quasi-isometries of horospherical products of hyperbolic spaces are geometrically rigid in the sense that they are uniformly close to product maps, this is a generalisation of the result obtained by Eskin, Fisher and Whyte in…

In this paper, we study the uniformities on the double coset spaces in topological groups. As an implication, the quotient spaces of topological groups with a $q$-point are studied. It mainly shows that: (1) Suppose that $G$ is a…

The groups QF, QT, and QV are groups of quasi-automorphisms of the infinite binary tree. Their names indicate a similarity with Thompson's well-known groups F, T, and V. We will use the theory of diagram groups over semigroup presentations…

We study those groups that act properly discontinuously, cocompactly, and isometrically on CAT(0) spaces with isolated flats and the Relative Fellow Traveller Property. The groups in question include word hyperbolic CAT(0) groups as well as…

We study groups of homeomorphic bijections on spaces that are finite unions of compact connected linearly ordered subsets. We prove that all such groups when endowed with the topology of point-wise convergence are topological groups. }

We define totally-isotropic polynomials of alternating matrix spaces over finite fields, by analogy with independence polynomials of graphs. Our main result shows that totally-isotropic polynomials of graphical alternating matrix spaces…