Finite rigid sets in flip graphs
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Abstract:
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.References
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Additional Information
- Emily Shinkle
- Affiliation: 1409 W Green St., Urbana, Illinois 61801
- MR Author ID: 1413648
- Email: emilyss2@illinois.edu
- Received by editor(s): November 8, 2020
- Received by editor(s) in revised form: February 8, 2021, and February 10, 2021
- Published electronically: December 2, 2021
- © Copyright 2021 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 375 (2022), 847-872
- MSC (2020): Primary 57K20, 20F65; Secondary 57M60, 05C60, 05C25
- DOI: https://doi.org/10.1090/tran/8407
- MathSciNet review: 4369237