Injective maps between flip graphs

Abstract

We prove that every injective simplicial map $\mathcal{F}(S)\to \mathcal{F}(S^{\prime })$ between flip graphs is induced by a subsurface inclusion $S\to S^{\prime }$, except in finitely many cases. This extends a result of Korkmaz--Papadopoulos which asserts that every automorphism of the flip graph of a surface without boundary is induced by a surface homeomorphism.

16 pages, 15 figures. To appear in Ann. Inst. Fourier