Finite Rigid Sets in Flip Graphs
Geometric Topology
2021-02-12 v2
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. We also include images of several flip graphs in an appendix.
Cite
@article{arxiv.2010.05363,
title = {Finite Rigid Sets in Flip Graphs},
author = {Emily Shinkle},
journal= {arXiv preprint arXiv:2010.05363},
year = {2021}
}
Comments
26 pages, 25 figures. Improved exposition and restructuring in Section 7. Expanded descriptions in Appendix. To appear in Transactions of the AMS