Related papers: Subgroups of the mapping class group from the geom…
We strengthen the analogy between convex co-compact Kleinian groups and convex co-compact subgroups of the mapping class group of a surface (in the sense of B. Farb and L. Mosher).
We investigate the separability of several well known classes of subgroups of the mapping class group of a surface.
This paper is a study of the subgroups of the mapping class groups of Riemann surfaces, called "geometric" subgroups, corresponding to the inclusion of subsurfaces. Our analysis includes surfaces with boundary and with punctures. The…
We focus on two kinds of infinite index subgroups of the mapping class group of a surface associated with a Lagrangian submodule of the first homology of a surface. These subgroups, called Lagrangian mapping class groups, are known to play…
In this article we survey, and make a few new observations about, the surprising connection between sub-monoids of mapping class groups and interesting geometry and topology in low-dimensions.
In this paper, we survey recent works on the structure of the mapping class groups of surfaces mainly from the point of view of topology. We then discuss several possible directions for future research. These include the relation between…
Let M be a surface (possibly nonorientable) with punctures and/or boundary components. The paper is a study of ``geometric subgroups'' of the mapping class group of M, that is subgroups corresponding to inclusions of subsurfaces (possibly…
We present a framework to determine subgroups of tetrahedron groups and tetrahedron Kleinian groups, based on tools in color symmetry theory.
The goal of these lectures is to give an introduction to the study of the fundamental group of a Klein surface. We start by reviewing the topological classification of Klein surfaces and by explaining the relation with real algebraic…
We give a brief overview of the current state of the study of the deformation theory of Kleinian groups. The topics covered include the definition of the deformation space of a Kleinian group and of several important subspaces; a discussion…
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 survey recent developments on mapping class groups of surfaces of infinite topological type.
We construct finite-dimensional projective representations of the mapping class groups of compact connected oriented surfaces having one boundary component using stated skein algebras.
We survey various constructions of finite dimensional projective representations of mapping class groups derived from stated skein algebras.
In this survey paper, we give a complete list of known results on the first and the second homology groups of surface mapping class groups. Some known results on higher (co)homology are also mentioned.
We prove that every finitely generated Kleinian group that contains a finite, non-cyclic subgroup either is finite or virtually free or contains a surface subgroup. Hence, every arithmetic Kleinian group contains a surface subgroup.
The present paper are the notes of a mini-course addressed mainly to non-experts. It purpose it to provide a first approach to the theory of mapping class groups of non-orientable surfaces.
This paper is a survey of the relationship between labelled configuration spaces, mapping class groups with marked points and function spaces. In particular, we collect calculations of the cohomology groups for the mapping class groups of…
The theme of this survey is that subgroups of the mapping class group of a finite type surface S can be studied via the geometric/dynamical properties of their action on the Thurston compactification of the Teichmuller space of S, just as…
We characterize convex cocompact subgroups of the mapping class group of a surface in terms of uniform convergence actions on the zero locus of the limit set. We also construct subgroups that act as uniform convergence groups on their limit…