The asymptotic dimension of a curve graph is finite

By Gregory C. Bell, K. Fujiwara. 2005

53 citations recorded by the source corpus.

We find an upper bound for the asymptotic dimension of a hyperbolic metric space with a set of geodesics satisfying a certain boundedness condition studied by Bowditch. The primary example is a collection of tight geodesics on the curve graph of a compact orientable surface. We use this to conclude that a curve graph has a finite asymptotic dimension. It follows then that a curve graph has property A1. We also compute the asymptotic dimension of mapping class groups of orientable surfaces with genus at most 2.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7404d41082bf1a20ce1be7561a2425e39cfa51fb

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Asymptotic Dimension (2007, methodology): “The extension theorem above (Theorem 68) was used by Bell and Fujiwara [11] in their upper bound estimates for mapping class groups of surfaces with genus at most 2:”
Tight geodesics in the curve complex (2008, background): “In [ BelF ], Bell and Fujiwara use Theorem 1.2 to show that G(Σ) has finite asymptotic dimension.”
Asymptotic dimension and small‐cancellation for hierarchically hyperbolic spaces and groups (2015, methodology): “To establish this bound for general (relatively) hierarchically hyperbolic spaces, we generalize the tight geodesics strategy of Bell Fujiwara [BF07], who proved that the asymptotic dimension of the curve graph of a surface of nite type is nite.”