Let M be a hyperbolic 3-manifold admitting a homotopy equivalence to a compact surface Sigma, where the cusps of M correspond exactly to the boundary components of Sigma. We construct a nested system of bands in M, where each band is homeomorphic to a subsurface of Sigma times an interval. This band system is shown to have various geometrical properties, notably that the boundary of any Margulis tube is mostly contained in the union of the bands. As a consequence, one can deduce the result (conjectured by McMullen and proven by Brock, Canary and Minsky) that the thick part of the convex core of M has at most polynomial growth. Moreover the degree is at most minus the Euler characteristic of Sigma. Other applications of this construction to the curve complex of Sigma will be discussed elsewhere. The complex is related to the block decomposition of M described by Minsky, in his work towards Thurston's Ending Lamination Conjecture.
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