Finite rigid subgraphs of the pants graphs of punctured spheres

Abstract

We prove a strong form of finite rigidity for pants graphs of spheres. Specifically, for any $n\ge 4$, we construct a finite subgraph $X_n$ of the pants graph $P(S_{0,n})$ of the n-punctured sphere $S_{0,n}$ with the following property. Any simplicial embedding of $X_n$ into any pants graph $P(S_{0,m})$ of a punctured sphere is induced by an embedding $S_{0,n}\to S_{0,m}$.

arXiv comment25 pages, 12 figures

Cited by in corpus (4)

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