Related papers: Normal generators for mapping class groups are abu…

In this paper we study the minimum dilatation pseudo-Anosov mapping classes coming from fibrations over the circle of a single 3-manifold, the mapping torus for the "simplest pseudo-Anosov braid". The dilatations that arise include the…

We give complete classification of C^2-regular and non-degenerate projectively Anosov flows on three dimensional manifolds. More precisely, we prove that such a flow on a connected manifold must be either an Anosov flow or represented as a…

We show that for $g\ge 2$, all integers $1 \le d \le 3g-3$ arise as trace field degrees of pseudo-Anosov mapping classes in the Torelli group of the closed orientable surface of genus $g$. Our method uses the Thurston-Veech construction of…

We give generators for a certain complex hyperbolic braid group. That is, we remove a hyperplane arrangement from complex hyperbolic $13$-space, take the quotient of the remaining space by a discrete group, and find generators for the…

By a theorem of Thurston, in the subgroup of the mapping class group generated by Dehn twists around two curves that fill, every element not conjugate to a power of one of the twist is pseudo-Anosov. We prove an analogue of this theorem for…

A group $G$ is said to be $\frac{3}{2}$-generated if every nontrivial element belongs to a generating pair. It is easy to see that if $G$ has this property then every proper quotient of $G$ is cyclic. In this paper we prove that the…

Let $\mathrm{Mod}(S_g)$ be the mapping class group of the closed orientable surface of genus $g \geq 1$. For $k \geq 2$, we consider the standard $k$-sheeted regular cover $p_k: S_{k(g-1)+1} \to S_g$, and analyze the liftable mapping class…

We study $6$-transposition groups, i.e. groups generated by a normal set of involutions $D$, such that the order of the product of any two elements from $D$ does not exceed $6$. We classify most of the groups generated by $3$ elements from…

Let $G$ be a finite group and $N$ a normal subgroup of $G$. We determine the structure of $N$ when the diameter of the graph associated to the $G$-conjugacy classes contained in $N$ is as large as possible, that is, is equal to three.

We give two explicit sets of generators of the group of invertible regular functions over QQ on the modular curve Y1(N). The first set of generators is very surprising. It is essentially the set of defining equations of Y1(k) for k <= N/2…

Let $N_{g,n}$ denote the closed non-orientable surface of genus $g$ with $n$ punctures and let ${\mathcal N}_{g,n}$ denote the mapping class group of $N_{g,n}$. Szepietowski showed that ${\mathcal N}_{g,n}$ is generated by finitely many…

The higher connectivity at infinity for mapping class groups of surfaces with boundary components and punctures is understood with the exceptions of the mapping class groups for the closed surfaces of genus 3 and 4. In this paper we prove a…

Let $S$ be a semigroup (written multiplicatively). Endowed with the operation of setwise multiplication induced by $S$ on its parts, the non-empty subsets of $S$ form themselves a semigroup, denoted by $\mathcal P(S)$. Accordingly, we say…

We prove that the mapping class group $\mathcal{M}(N_g)$ of a closed nonorientable surface of genus $g$ different than 4 is generated by three torsion elements. Moreover, for every even integer $k\ge 12$ and $g$ of the form $g=pk+2q(k-1)$…

Generalizing the classification approach described for transitive Anosov flows in dimension 3 in a previous preprint of the author, in this paper we describe a method for classifying (not necessarily transitive) pseudo-Anosov flows on…

Dujmovi\'c et al. [\emph{J.~ACM}~'20] recently proved that every planar graph is isomorphic to a subgraph of the strong product of a bounded treewidth graph and a path. Analogous results were obtained for graphs of bounded Euler genus or…

A pseudo-Anosov homeomorphism of a surface is a canonical representative of its mapping class. In this paper, we explain that a transitive pseudo-Anosov flow is similarly a canonical representative of its stable Hamiltonian class. It…

Dynamical semigroups have become the key structure for describing open system dynamics in all of physics. Bounded generators are known to be of a standard form, due to Gorini, Kossakowski, Sudarshan and Lindblad. This form is often used…

In this paper we prove that finite index subgroups of genus 3 mapping class and Torelli groups that contain the group generated by Dehn twists on bounding simple closed curves are not Kahler. These results are deduced from explicit…

Let $\textrm{Mod}(N_{g, p})$ denote the mapping class group of a nonorientable surface of genus $g$ with $p$ punctures. For $g\geq14$, we show that $\textrm{Mod}(N_{g, p})$ can be generated by five elements or by six involutions.