相关论文: Roots of Dehn twists about separating curves

Margalit and Schleimer observed that Dehn twists on orientable surfaces have nontrivial roots. We investigate the problem of roots of a Dehn twist t_c about a nonseparating circle c in the mapping class group M(N_g) of a nonorientable…

A \textit{multicurve} $\C$ on a closed orientable surface is defined to be a finite collection of disjoint non-isotopic essential simple closed curves. The Dehn twist $t_{\C}$ about $\C$ is the product of the Dehn twists about the…

Margalit and Schleimer constructed nontrivial roots of the Dehn twist about a nonseparating curve. We prove that the conjugacy classes of roots of the Dehn twist about a nonseparating curve correspond to the conjugacy classes of periodic…

D. Margalit and S. Schleimer found examples of roots of the Dehn twist about a nonseparating curve in a closed orientable surface, that is, homeomorphisms whose nth power is isotopic to the Dehn twist. Our main theorem gives elementary…

Let $S_g$ denote a closed, orientable surface of genus $g \geq 2$ and $\mathcal{C}(S_g)$ be the associated curve complex. The mapping class group of $S_g$, $Mod(S_g)$ acts on $\mathcal{C}(S_g)$ by isometries. Since Dehn twists about certain…

We construct nontrivial roots of Dehn twists about nonseparating curves.

Let $\text{Mod}(S_g)$ be the mapping class group of the closed orientable surface $S_g$ of genus $g \geq 1$. In this paper, we develop various methods for factoring periodic mapping classes into Dehn twists, up to conjugacy. As…

Let $N_{g}$ denote a closed nonorientable surface of genus $g$. For $g \geq 2$ the mapping class group $\mathcal{M}(N_{g})$ is generated by Dehn twists and one crosscap slide ($Y$-homeomorphism) or by Dehn twists and a crosscap…

For $g\geq 2$, let $\mathrm{Mod}(S_g)$ be the mapping class group of the closed orientable surface $S_g$ of genus $g$. In this paper, we obtain necessary and sufficient conditions under which a given pseudo-periodic mapping class can be a…

Consider the following classes of pairs consisting of a group and a finite collection of subgroups: $\mathcal{C}= \left\{ (G,\mathcal H) \mid \text{$\mathcal{H}$ is hyperbolically embedded in $G$} \right\}$ and $ \mathcal{D}= \left\{…

Let $N_g^k$ be a nonorientable surface of genus \ $g\geq 5$ \ with \ $k$-punctures. In this note, we will give an algebraic characterization of a Dehn twist about a simple closed curve on $N_g^k$. Along the way, we will fill some little…

We give new upper bounds on the stable commutator lengths of Dehn twists along separating curves in the mapping class group of a closed oriented surface. The estimates of these upper bounds are $O(1/g)$, where $g$ is the genus of the…

We calculate the Dehn twist action on the spaces of conformal blocks of a not necessarily semisimple modular category. In particular, we give the order of the Dehn twists under the mapping class group representations of closed surfaces. For…

Let $S_g$ denote a closed oriented surface of genus $g \geq 2$. A set $\Omega = \{ c_1, \dots, c_d\}$ of pairwise non-homotopic simple closed curves on $S_g$ is called a filling system or simply a filling of $S_g$, if $S_g\setminus \Omega$…

Let $S_g$ be a closed orientable surface of genus $g \geq 2$ and $C$ a simple closed nonseparating curve in $F$. Let $t_C$ denote a left handed Dehn twist about $C$. A \textit{fractional power} of $t_C$ of \textit{exponent}…

The first aim of this paper is to give four types of examples of surface bundles over surfaces with non-zero signature. The first example is with base genus 2, a prescribed signature, a 0-section and the fiber genus greater than a certain…

Let $S_g$ denote a closed, orientable surface of genus $g \geq 2$ and $\mathcal{C}(S_g)$ be the associated curve graph. Let $d$ be the path metric on $\mathcal{C}(S_g)$ and $a_0$ and $a_4$ be a pair of curves on $S_g$ with $d(a_0, a_4) =…

The level $2$ mapping class group of an orientable closed surface can be generated by squares of Dehn twists about non-separating curves. On the other hand, the level $2$ mapping class group $\mathcal{M}_2(N_g)$ of a non-orientable closed…

We prove cyclic sieving phenomena satisfied by corner-rooted plane trees (alias ordered trees). The sets of rooted plane trees that we consider are: (1) all trees with $n$ nodes; (2) all trees with $n$ nodes and $k$ leaves; (3) all trees…

We consider the family of Heegaard splittings of genus $g$ at least three which are defined via a glueing map that is the $n$-th power of the Dehn twist along a curve that satisfies a natural topological assumption, namely pared…