Big Mapping Class Groups: An Overview | SpringerLink Skip to main content Advertisement
SpringerLink Account Menu Find a journal Publish with us Track your research Search Cart …

We study the large-scale geometry of mapping class groups of surfaces of infinite type, using
the framework of Rosendal for coarse geometry of non-locally-compact groups. We give a …

Let S be an orientable, connected topological surface of infinite type (that is, with infinitely
generated fundamental group). The main theorem states that if the genus of S is finite and at …

It is a classical result that pure mapping class groups of connected, orientable surfaces of
finite type and genus at least 3 are perfect. In stark contrast, we construct nontrivial …

Given a 2-manifold, a fundamental question to ask is which groups can be realized as the
isometry group of a Riemannian metric of constant curvature on the manifold. In this paper …

We prove that if a normal subgroup of the extended mapping class group of a closed surface
has an element of sufficiently small support, then its automorphism group and abstract …

ISOMORPHISMS BETWEEN CURVE GRAPHS OF INFINITE-TYPE SURFACES ARE
GEOMETRIC 1. Introduction. This is the last of three papers on t Page 1 ROCKY MOUNTAIN …

We address the question of determining which mapping class groups of infinite-type
surfaces admit nonelementary continuous actions on hyperbolic spaces. More precisely, let …

A theorem of Farb and Handel [Publ. Math. Inst. Hautes Études Sci. 105 (2007), pp. 1–48]
asserts that for $ N\ge 4$, the natural inclusion from $\mathrm {Out}(F_N) $ into its abstract …

We describe the topological behavior of the conjugacy action of the mapping class group of
an orientable infinite-type surface $\Sigma $ on itself. Our main results are:(1) All conjugacy …