Asymptotic dimension and the disk graph I

Abstract

For a 3-manifold M and a subsurface $X$ of the boundary of M with empty or incompressible boundary we use surgery to identify a graph whose vertices are disks with boundary in X and which is quasi-isometrically embedded in the curve graph of X.

17 pages, 1 figure

References in corpus (8)

• Train tracks and the Gromov boundary of the complex of curves
• On metric relative hyperbolicity
• Geometry of the mapping class group II: A biautomatic structure
• On the geometry of a proposed curve complex analogue for $Out(F_n)$
• Automorphisms of the graph of free splittings
• Distance in the Ellipticity Graph
• Asymptotic dimension and the disk graph II
• Distance in the curve graph

Cited by in corpus (7)

• The boundary of the free splitting graph and the free factor graph
• Asymptotic dimension and the disk graph II
• The Powell Conjecture and reducing sphere complexes
• Hyperbolicity of the graph of non-separating multicurves
• Goeritz groups of bridge decompositions
• Problems on handlebody groups
• Spotted disk and sphere graphs I