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Finite Rigid Sets in Flip Graphs

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arxiv 2010.05363 v2 pith:7YSQG3LG submitted 2020-10-11 math.GT

Emily Shinkle This is my paper · ORCID
classification math.GT
keywords flipfinitegraphshomomorphisminjectivegraphsubgraphsurface
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We show that for most pairs of surfaces, there exists a finite subgraph of the flip graph of the first surface so that any injective homomorphism of this finite subgraph into the flip graph of the second surface can be extended uniquely to an injective homomorphism between the two flip graphs. Combined with a result of Aramayona-Koberda-Parlier, this implies that any such injective homomorphism of this finite set is induced by an embedding of the surfaces. We also include images of several flip graphs in an appendix.

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