Finite rigid subgraphs of pants graphs

Abstract

Let $S_{g,n}$ be an orientable surface of genus $g$ with $n$ punctures. We identify a finite rigid subgraph $X_{g,n}$ of the pants graph $\mathcal{P}(S_{g,n})$, that is, a subgraph with the property that any simplicial embedding of $X_{g,n}$ into any pants graph $\mathcal{P}(S_{g^{\prime },n^{\prime }})$ is induced by an embedding $S_{g,n}\to S_{g^{\prime },n^{\prime }}$. This extends results of the third author for the case of genus zero surfaces.

18 pages, 14 figures. Geom Dedicata (2020)