On the asymptotic dimension of the curve complex

Abstract

We give a bound, linear in the complexity of the surface, on the asymptotic dimension of the curve complex as well as the capacity dimension of the ending lamination space.

The main change in this version is that in a number of the lemmas on train tracks the tracks are no longer assumed to be recurrent. This led to a significant revision of section 3 of the paper. To appear in Geometry and Topology

References in corpus (2)

• Asymptotic dimension and small-cancellation for hierarchically hyperbolic spaces and groups
• Embedding relatively hyperbolic groups in products of trees

Cited by in corpus (3)

• Stability and the Morse boundary
• On the topological dimension of the Gromov boundaries of some hyperbolic $Out(F_N)$-graphs
• Asymptotic dimensions of the arc graphs and disk graphs