相关论文: Orderings of mapping class groups after Thurston
We give an alternate proof of the left-orderability of the mapping class group of a connected oriented infinite-type surface with a non-empty boundary. Our main strategy involves the inductive construction of a countable stable Alexander…
We are concerned with orderable groups and particularly those with orderings invariant not only under multiplication, but also under a given automorphism or family of automorphisms. Several applications to topology are given: we prove that…
We show that the pure mapping class group is uniformly perfect for a certain class of infinite type surfaces with noncompact boundary components. We then combine this result with recent work in the remaining cases to give a complete…
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…
We study the action of the mapping class group on the real homology of finite covers of a topological surface. We use the homological representation of the mapping class to construct a faithful infinite-dimensional representation of the…
The action of the mapping class group of a surface on the collection of homotopy classes of disjointly embedded curves or arcs in the surface is discussed here as a tool for understanding Riemann's moduli space and its topological and…
A left orderable completely metrizable topological group is exhibited containing Artin's braid group on infinitely many strands. The group is the mapping class group (rel boundary) of the closed unit disk with a sequence of interior…
We study mapping class group orbits of homotopy and isotopy classes of curves with self-intersections. We exhibit the asymptotics of the number of such orbits of curves with a bounded number of self-intersections, as the complexity of the…
We show that the natural map from the mapping class groups of surfaces to the automorphism groups of free groups, induces an infinite loop map on the classifying spaces of the stable groups after plus construction. The proof uses…
We show how to use topological ideas, such as compactness, to establish orderability properties of infinite groups. A new application is to provide a left-ordering for the group of PL homeomorphisms of a connected surface with boundary…
The relationships between braid ordering and the geometry of its closure is studied. We prove that if an essential closed surface $F$ in the complements of closed braid has relatively small genus with respect to the Dehornoy floor of the…
We obtain some classification result for the mapping class groups of compact orientable surfaces in terms of measure equivalence. In particular, the mapping class groups of different closed surfaces can not be measure equivalent. Moreover,…
We study the action of the elements of the mapping class group of a surface of finite type on the Teichm\"uller space of that surface equipped with Thurston's asymmetric metric. We classify such actions as elliptic, parabolic, hyperbolic…
Thurston maps are branched self-coverings of the sphere whose critical points have finite forward orbits. We give combinatorial and algebraic characterizations of Thurston maps that are isotopic to expanding maps as "Levy-free" maps and as…
This paper has three parts. The first part is a general introduction to rigidity and to rigid actions of mapping class group actions on various spaces. In the second part, we describe in detail four rigidity results that concern actions of…
There exist right angled Artin groups $A$ such that the isomorphism problem for finitely presented subgroups of $A$ is unsolvable, and for certain finitely presented subgroups the conjugacy and membership problems are unsolvable. It follows…
For any left orderable group G, we recall from work of McCleary that isolated points in the space of left orderings correspond to basic elements in the free lattice ordered group over G. We then establish a new connection between the…
We explicitly construct new subgroups of the mapping class groups of an uncountable collection of infinite-type surfaces, including, but not limited to, free groups, Baumslag-Solitar groups, mapping class groups of other surfaces, and a…
We show that for any $k$ at least $6$ and $g$ sufficiently large, the mapping class group of a surface of genus $g$ can be generated by three elements of order $k$. We also show that this can be done with four elements of order $5$. We…
We obtain simple generating sets for various mapping class groups of a nonorientable surface with punctures and/or boundary. We also compute the abelianizations of these mapping class groups.