The Pants Graph of a Free Group
arXiv:2410.15276 · doi:10.1112/topo.70078
Abstract
We introduce the concept of a pants decomposition for a finitely generated free group and construct the corresponding pants graph. A pants decomposition of a free group leads to the formation of a simplicial graph, referred to as the pants graph of a free group, consisting of all possible pants decompositions. The natural isometric action of the outer automorphism group of the free group on the pants graph induces a coarsely surjective orbit map. Additionally, we construct a coarsely Lipschitz map from the pants graph to the free splitting complex. These results imply that the pants graph of a free group is both connected and unbounded.
18 pages, 10 figures, Comments are welcome!