Train tracks, distance in the curve complex and the capacity dimension of the space of ending laminations

Ken Bromberg (Utah)

Abstract: We will give a linear upper bound on the capacity dimension of the space of ending laminations, Buyalo has shown that the asymptotic dimension of a hyperbolic space is bounded by one plus the capacity dimension of it's boundary so this also gives a linear bound on the asymptotic dimension of the curve complex. The key tool is an estimate on distance in the curve complex for curves supported on a train track. This is joint work with Mladen Bestvina.