The Tri-Pants Graph of the Twice-Punctured Torus
Geometric Topology
2021-11-16 v1
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.
Cite
@article{arxiv.2111.07136,
title = {The Tri-Pants Graph of the Twice-Punctured Torus},
author = {Katherine Betts and Troy Larsen and Jeffrey Utley and Avalon Vanis},
journal= {arXiv preprint arXiv:2111.07136},
year = {2021}
}
Comments
32 pages, 19 figures