Related papers: Mapping class group is generated by three involuti…
This paper is the second part of a two-part study of an elementary functorial construction of tesselated surfaces from finite groups. This elementary construction was discussed in the first part and generally results in a large collection…
We show that for a closed surface of genus at least 5, or a surface of genus at least 2 with at least one marked point, the set of uniquely ergodic foliations and the set of cobounded foliations is path-connected and locally path-connected.
We consider finite-sheeted, regular, possibly branched covering spaces of compact surfaces with boundary and the associated liftable and symmetric mapping class groups. In particular, we classify when either of these subgroups coincides…
It is shown that each integrable mapping is connected with a hierarchical completely integrable sytem of equations of evolution type which are invariant with respect to the transformation described by this mapping.
A method is suggested for construction of quadrangulations of the closed orientable surface with given genus g and either (1) with given chromatic number or (2) with given order allowed by the genus g. In particular, N. Hartsfield and G.…
Omori and the author have given an infinite presentation for the mapping class group of a compact non-orientable surface. In this paper, we give more simple infinite presentations for this group.
A conjecture of Broaddus is proven, giving a simple characterisation of a representative of the unique orbit of the action of the mapping class group on the homology of Harvey's complex of curves for any genus surface. As an application,…
We show that Szepietowski's system of generators for the mapping class group of a non-orientable surface is a minimal generating set by Dehn twists and $Y$-homemorphisms.
We determine the first homology group with coefficients in $H_1(N;\mathbb{Z})$ for the mapping class group of a non-orientable surface $N$ of genus three with two boundary components.
For $\Sigma$ an orientable surface of finite topological type having genus at least 3 (possibly closed or possibly with any number of punctures or boundary components), we show that the mapping class group $Mod(\Sigma)$ has no faithful…
We prove that any permutation group of degree $n \geq 4$ has at most $5^{(n-1)/3}$ conjugacy classes.
We construct a minimal generating set of the level 2 mapping class group of a nonorientable surface of genus $g$, and determine its abelianization for $g\ge4$.
In this work, we study three families of locally graded groups with finitely many orbits under automorphisms. We prove that: (i) a residually finite group with finitely many orbits under automorphisms is locally finite and has finite…
We provide numerical evidence that the orbit closure of the unfolding of the $(3,4,13)$-triangle is a previously unknown 4-dimensional variety.
We are concerned with mapping class groups of surfaces with nonempty boundary. We present a very natural method, due to Thurston, of finding many different left orderings of such groups. The construction involves equipping the surface with…
Eight different refinements of trapped surfaces are proposed, of three basic types, each intended as potential stability conditions. Minimal trapped surfaces are strictly minimal with respect to the dual expansion vector. Outer trapped…
For each closed orientable surface we introduce a simplical complex with some additional structure which is a version of the complex of curves of this surface adjusted to investigation of its Torelli group. We call this complex the Torelli…
When $S$ is a closed, orientable surface with genus $g(S) \geq 2$, we show that the automorphism group of the compression body graph $\mathcal{CB}(S)$ is the mapping class group. Here, vertices are compression bodies with exterior boundary…
We prove that fundamental groups of orientable (geometrizable) 3-manifolds have a solvable conjugacy problem.
We construct the first known examples of nontrivial, normal, all pseudo-Anosov subgroups of mapping class groups of surfaces. Specifically, we construct such subgroups for the closed genus two surface and for the sphere with five or more…