Constructing convex planes in the pants complex
Shackleton, Kenneth J.
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Aramayona, Javier; Parlier, Hugo; Shackleton, Kenneth J. (2009). Constructing convex planes in the pants complex. Proceedings of the American Mathematical Society 137 (10), 3523-3531
Our main theorem identifies a class of totally geodesic subgraphs of the 1-skeleton of the pants complex, referred to as the pants graph, each isomorphic to the product of two Farey graphs. We deduce the existence of many convex planes in the pants graph of any surface of complexity at least 3.