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The augmented marking complex of a surface

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, 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 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 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.