Related papers: General primitivity in the mapping class group

We study torsion generators for the (extended) mapping class group or the extended mapping class group of a closed connected orientable surface of genus g. We show that for every g is grater than or equal to 14, mapping class group can be…

Given $G$ an algebraic reductive group over an algebraically closed field of characteristic zero and $\Gamma$ a finitely generated group, we provide a stratification of the $G$-character variety of $\Gamma$ in terms of conjugacy classes of…

We provide a simple criterion for an element of the mapping class group of a closed surface to have normal closure equal to the whole mapping class group. We apply this to show that every nontrivial periodic mapping class that is not a…

We consider (local) parametrizations of Teichmuller space $T_{g,n}$ (of genus $g$ hyperbolic surfaces with $n$ boundary components) by lengths of $6g-6+3n$ geodesics. We find a large family of suitable sets of $6g-6+3n$ geodesics, each set…

Recently, Korkmaz established the lower bound of $3g - 2$ for the dimension of a faithful representation of the mapping class group of an orientable surface of genus $g \ge 3$. We raise this bound to $4g - 3$ in the setting of surfaces of…

We prove that the mapping class group of a closed connected orientable surface of genus $g$ is generated by two elements of order $g$ for $g\geq 6$. Moreover, for $g\geq 7$ we found a generating set of two elements, of order $g$ and $g'$…

Suppose $f$ and $g$ are two post-critically finite polynomials of degree $d_1$ and $d_2$ respectively and suppose both of them have a finite super-attracting fixed point of degree $d_0$. We prove that one can always construct a rational map…

We study subsets in possibly degenerate symplectic vector spaces over finite fields, which are stable under a given Coxeter/Weyl reflection group. These symplectic root systems provide crucial combinatorical data to classify…

Let $S$ be a nonorientable surface of genus $g\ge 5$ with $n\ge 0$ punctures, and $\Mcg(S)$ its mapping class group. We define the complexity of $S$ to be the maximum rank of a free abelian subgroup of $\Mcg(S)$. Suppose that $S_1$ and…

We study in detail the profinite group G arising as geometric \'etale iterated monodromy group of an arbitrary quadratic morphism f with an infinite postcritical orbit over a field of characteristic different from two. This is a…

Let $s$ be a fixed hyperelliptic involution of the closed, oriented genus $g$ surface $\Sigma_g$. The hyperelliptic Torelli group $\mathcal{SI}_g$ is the subgroup of the mapping class group $\mathrm{Mod}(\Sigma_g)$ consisting of elements…

Let f be a Z/2Z-spin structureon a closed surface S of genus g>3. We determine a generating set of the stabilizer of f in the mapping class group of S consisting of Dehn twists about an explicit collection of 2g+1 curves in S. If g=3 then…

Given a hyperbolic surface $\Sigma$ of genus $g$ with $r$ cusps, Mirzakhani proved that the number of closed geodesics of length at most $L$ and of a given type is asymptotic to $cL^{6g-6+2r}$ for some $c>0$. Since a closed geodesic…

Given any connected compact orientable surface, a pair of mapping classes are said to be procongruently conjugate if they induce a conjugate pair of outer automophisms on the profinite completion of the fundamental group of the surface. For…

Let $N_{g}$ denote the closed non-orientable surface of genus $g$ and let ${\mathcal M} _g$ denote the mapping class group of $N_{g}$. Let ${\mathcal T} _g$ denote the twist subgroup of ${\mathcal M} _g$ which is the subgroup of ${\mathcal…

Let Ng be the connected closed nonorientable surface of genus g >= 5 and Mod(Ng) denote the mapping class group of Ng. We prove that the outer automorphism group of Mod(Ng) is either trivial or Z if g is odd, and injects into the mapping…

Let $\Sigma_{g,b}$ denote a closed orientable surface of genus $g$ with $b$ punctures and let $\rm Mod(\Sigma_{\textit{g,b}})$ denote its mapping class group. In [Luo] Luo proved that if the genus is at least 3, $\rm…

A subperiodic group is a group of motions of $d$-dimensional Euclidean space $\R^d$ which contains a translation lattice $\Z^r$ of rank $r < d$ as a subgroup of finite index. A classification into abstract group isomorphism classes is…

The germ of the universal isomonodromic deformation of a logarithmic connection on a stable n-pointed genus g curve always exists in the analytic category. The first part of this paper investigates under which conditions it is the analytic…

In this paper, we set $\eta (G)$ to be the number of conjugacy classes of maximal cyclic subgroups of a finite group $G$. We compute $\eta (G)$ for all metacyclic $p$-groups. We show that if $G$ is a metacyclic $p$-group of order $p^n$ that…