Related papers: Continuum of allosteric actions for non-amenable s…

We generalise results about isometric group actions on metric spaces and their fundamental regions to the context of merely continuous group actions. In particular, we obtain results that yield the relative compactness of a fundamental…

We construct a Riemannian metric $g$ on $\mathbb{R}^4$ (arbitrarily close to the euclidean one) and a smooth simple closed curve $\Gamma\subset \mathbb R^4$ such that the unique area minimizing surface spanned by $\Gamma$ has infinite…

This note studies the Burnside problem for homeomorphism groups of compact connected manifolds. For surfaces, we prove that the identity component of the homeomorphism group is torsion-free precisely when the surface is not the sphere,…

We show that given any subgroup F of R_+ which is either countable or belongs to a certain "large" class of uncountable subgroups, there exist continuously many free ergodic probability measure preserving actions \sigma_i of the free group…

In this paper we prove that if two normal affine surfaces $S$ and $S'$ have isomorphic automorphism groups, then every connected algebraic group acting regularly and faithfully on $S$ acts also regularly and faithfully on $S'$. Moreover, if…

In this paper we use free iterated actions and the iterated discrete degree of symmetry to obtain rigidity results on aspherical manifolds. We also introduce the concept of the length of an iterated action and we study it for nilmanifolds,…

A measure preserving action of a countably infinite group \Gamma is called totally ergodic if every infinite subgroup of \Gamma acts ergodically. For example, all mixing and mildly mixing actions are totally ergodic. This note shows that if…

A free action of a finite group on an odd-dimensional sphere is said to be almost linear if the action restricted to each cyclic or 2-hyperelementary subgroup is conjugate to a free linear action. We begin this survey paper by reviewing the…

The purpose of this article is to characterize symplectic and Hamiltonian circle actions on symplectic manifolds in terms of symplectic embeddings of Riemann surfaces. More precisely, we will show that (1) if $(M,\omega)$ admits a…

In this note, we lay the groundwork for a new approach to the problem of group-signature classification of group actions on closed Riemann surfaces. This new approach first focuses on analyzing the low level arithmetic conditions on…

For plane frameworks with reflection or rotational symmetries, where the group action is not necessarily free on the vertex set, we introduce a phase-symmetric orbit rigidity matrix for each irreducible representation of the group. We then…

It was proved by Tien-Cuong Dinh and me that there is a smooth complex projective surface whose automorphism group is discrete and not finitely generated. In this paper, we will show that there is a smooth projective surface, birational to…

By an additive action on an algebraic variety $X$ we mean a regular effective action $\mathbb{G}_a^n\times X\to X$ with an open orbit of the commutative unipotent group $\mathbb{G}_a^n$. In this paper, we give a classification of additive…

The automorphisms of a two-generator free group acting on the space of orientation-preserving isometric actions of on hyperbolic 3-space defines a dynamical system. Those actions which preserve a hyperbolic plane but not an orientation on…

The fundamental group of every surface that is not the projective plane or Klein bottle has a representation to a torsion-free group of upper-triangular matrices in SL(2,R) with no simple loop (i.e. a nontrivial element representing a…

In this paper we study a natural generalization of symplectic toric manifolds in the context of regular Poisson manifolds of compact types. To be more precise, we consider a class of multiplicity-free Hamiltonian actions by regular proper…

Let $\Gamma$ be an amenable countable discrete group. Fix an ergodic free nonsingular action of $\Gamma$ on a nonatomic standard probability space. Let $G$ be a compactly generated locally compact second countable group such that the…

We describe the structure of the free actions of the Klein bottle group by orientation preserving homeomorphisms of the plane. This group is generated by two elements $a,b$, where the conjugate of $b$ by $a$ equals the inverse of $b$. The…

We determine all finite maximal elementary abelian group actions on compact oriented surfaces of genus $\sigma\geq 2$ which are unique up to topological equivalence. For certain special classes of such actions, we determine group extensions…

Consider two free measure preserving group actions $\Gamma \actson (X, \mu), \Delta \actson (X, \mu)$, and a measure preserving action $\Delta \actson^a (Z, \nu)$ where $(X, \mu), (Z, \nu)$ are standard probability spaces. We show how to…