One of the more natural candidates for a theory that would encompass both nonpositively curved cube complexes and simplicial nonpositive curvature is the study of (suitably restricted) complexes built out of direct products of regular simplices. And a natural test case for the theory is whether one can prove a (bi)automaticity result using a language that generalizes the natural languages in the two motivating cases. Rena Levitt and I have been investigating the 2-dimensional base case of such a grand unification program and the results are somewhat subtle and surprising. My talk will mostly focus on nonpositively curved 2-complexes built out of triangles and squares with some comments on their higher dimensional generalizations.

Lecture #12557

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