2021/11/13 by Betts, Katherine, Larsen, Troy, Utley, Jeffrey +1
#57K20 #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2111.07136
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.