Abstract

We build an augmentation of the Masur–Minsky marking complex by Groves-Manning combinatorial horoballs to obtain a graph we call the augmented marking complex, $$\mathcal {AM}(S)$$. Adapting work of Masur–Minsky, we show that this augmented marking complex is quasiisometric to Teichmüller space with the Teichmüller metric. A similar construction was independently discovered by Eskin–Masur–Rafi. We also completely integrate the Masur–Minsky hierarchy machinery to $$\mathcal {AM}(S)$$ to build flexible families of uniform quasigeodesics in Teichmüller space. As an application, we give a new proof of Rafi's distance formula for $$\mathcal {T}(S)$$ with the Teichmüller metric. We have included an appendix, in which we prove a number of facts about hierarchies that we hope will be of independent interest.

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