Extensions of finitely generated Veech groups
Abstract
Given a closed surface S with finitely generated Veech group G and its 1 .S/-extension , there exists a hyperbolic space b E on which acts isometrically and cocompactly.The space bE is obtained by collapsing some regions of the surface bundle over the convex hull of the limit set of G. Using the nice action of on the hyperbolic space b E, it is shown that is hierarchically hyperbolic.These are generalizations of Dowdall-Durham-Leininger-Sisto, who assume in addition that G is a lattice.Because finitely generated Veech groups are among the most basic examples of subgroups of mapping class groups which are expected to qualify as geometrically finite, this result is evidence for the development of a broader theory of geometric finiteness.
Fields of Study & Subjects
Geometric and Algebraic Topology
Publication details
- Journal / source
- Algebraic & Geometric Topology
- Volume
- 26
- Issue
- 3
- Pages
- 989–1035
- Publication date
- 1 April 2026
- Language
- EN