The Tri-Pants Graph of the Twice-Punctured Torus

Katherine Betts; Troy Larsen; Jeffrey Utley; Avalon Vanis

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arXiv · 2111.07136

The Tri-Pants Graph of the Twice-Punctured Torus

Katherine Betts·Troy Larsen·Jeffrey Utley·Avalon Vanis

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Abstract

We investigate the structure of the tri-pants graph, a simplicial graph introduced by Maloni and Palesi, whose vertices correspond to particular collections of homotopy classes of simple closed curves of the twice-punctured torus, called tri-pants, and whose edges connect two vertices whenever the corresponding pants differ by suitable elementary moves. In particular, by examining the relationship between the tri-pants graph and the dual of the Farey complex, we prove that the tri-pants graph is connected and has infinite diameter.

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Katherine Betts, Troy Larsen, Jeffrey Utley, Avalon Vanis. 2021-11-13. The Tri-Pants Graph of the Twice-Punctured Torus. https://arxiv.org/abs/2111.07136

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