Related papers: The Mapping Class Group of a Minimal Subshift

We show that continuous epimorphisms between a class of subgroups of mapping class groups of orientable infinite-genus 2-manifolds with no planar ends are always induced by homeomorphisms. This class of subgroups includes the pure mapping…

We adapt a construction of Gabrielov and Vorobjov for use in the symmetric case. Gabrielov and Vorobjov had developed a means by which one may replace an arbitrary set $S$ definable in some o-minimal expansion of $\mathbb{R}$ with a compact…

We study a class $\mathfrak{M}$ of cyclically presented groups that includes both finite and infinite groups and is defined by a certain combinatorial condition on the defining relations. This class includes many finite metacyclic…

Let $M(N_{h,n})$ denote the mapping class group of a compact nonorientable surface of genus $h\ge 7$ and $n\le 1$ boundary components, and let $T(N_{h,n})$ be the subgroup of $M(N_{h,n})$ generated by all Dehn twists. It is known that…

For a metric space $X$ we study metrics on the two copies of $X$. We define composition of such metrics and show that the equivalence classes of metrics are a semigroup $M(X)$ Our main result is that $M(X)$ is an inverse semigroup,…

We use the structure theory of minimal dynamical systems to show that, for a general group $\Gamma$, a tame, metric, minimal dynamical system $(X, \Gamma)$ has the following structure: \begin{equation*} \xymatrix {& \tilde{X} \ar[dd]_\pi…

Topological dynamical systems $(X,T)$ are actions $T \times X \to X$, given as $(t, x) \to tx$, on a compact, Hausdorff topological space $X$ with $T$ as an acting group or monoid. We take up the property of topological transitivity…

The group of automorphisms of a symbolic dynamical system is countable, but often very large. For example, for a mixing subshift of finite type, the automorphism group contains isomorphic copies of the free group on two generators and the…

Let $\textup{H}_g$ be a genus $g$ handlebody and $\textup{MCG}_{2n}(\textup{T}_g)$ be the group of the isotopy classes of orientation preserving homeomorphisms of $\textup{T}_g=\partial\textup{H}_g$, fixing a given set of $2n$ points. In…

Let $M$ be a compact surface with boundary. We are interested in the question of how a group action on $M$ permutes a finite invariant set $X \subset int(M)$. More precisely, how the algebraic properties of the induced group of permutations…

Let $M$ be a compact connected orientable Seifert manifold with hyperbolic orbifold $B_M$, and $f_{\pi}: \pi_1(M)\rightarrow\pi_1(M)$ be an automorphism induced by an orientation-reversing homeomorphism $f$ of $M$. We give a bound on the…

To a Toeplitz flow $(X,T)$ we associate an ordered $K^0$-group, denoted $K^0(X,T)$, which is order isomorphic to the $K^0$-group of the associated (non-commutative) $C^\ast$-crossed product $C(X)\rtimes_T \mathbb{Z}$. However, $K^0(X,T)$…

For any $C\in[0,\infty]$ a compact group automorphism $T:X\to X$ is constructed with the property that $$ \frac{1}{n}\log|\{x\in X\mid T^n(x)=x\}|\longrightarrow C. $$ This may be interpreted as a combinatorial analogue of the (still open)…

The mapping class group of a surface with one boundary component admits numerous interesting representations including as a group of automorphisms of a free group and as a group of symplectic transformations. Insofar as the mapping class…

Let $M$ be a compact surface and $P$ be either $\mathbb{R}$ or $S^1$. For a smooth map $f:M\to P$ and a closed subset $V\subset M$, denote by $\mathcal{S}(f,V)$ the group of diffeomorphisms $h$ of $M$ preserving $f$, i.e. satisfying the…

Let $B$ be Banach algebra and $M$ be topological space. If there exists homeomorphism \[ f:M\rightarrow N \] of topological space $M$ into convex set $N$ of the space $B^n$, then homeomorphism $f$ is called chart of the set $M$. The set $M$…

We show that a natural class of twistorial maps gives a pattern for apparently different geometric maps, such as, $(1,1)$-geodesic immersions from $(1,2)$-symplectic almost Hermitian manifolds and pseudo horizontally conformal submersions…

A family $\mathcal L$ of subsets of a set $X$ is called linked if $A\cap B\ne\emptyset$ for any $A,B\in\mathcal L$. A linked family $\mathcal M$ of subsets of $X$ is maximal linked if $\mathcal M$ coincides with each linked family $\mathcal…

A countable family of $*$-commuting surjective, non-injective local homeomorphisms of a compact Hausdorff space $X$ gives rise to an action $\theta$ of a countably generated, free abelian monoid $P$. For such a triple $(X,P,\theta)$, which…

Let $M$ be a compact, connected manifold of positive dimension and let $\mathcal G\leq\textrm{Homeo}(M)$ be \emph{locally approximating} in the sense that for all open $U\subseteq M$ compactly contained in a single Euclidean chart of $M$,…