Rigidity of the saddle connection complex - Disarlo, Valentina; Randecker, Anja; Tang, Robert (Journal of topology, 2022)
For a half-translation surface (S,q)$(S,q)$, the associated saddle connection complex A(S,q)$\mathcal A(S,q)$ is the simplicial complex where vertices are the saddle connections on (S,q)$(S,q)$, with simplices spanned by sets of pairwise disjoint saddle connections. This complex can be naturally regarded as an induced subcomplex of the arc complex. We prove that any simplicial isomorphism ϕ:A(S,q)→A(S′,q′)$φ \colon \mathcal A(S,q) → \mathcal A(S^′ ,q^′ )$ between saddle connection complexes is induced by an affine diffeomorphism F:(S,q)→(S′,q′