Rigidity of the saddle connection complex


For a half-translation surface (S,q), the associated \emphsaddle connection complex \A(S,q) is the simplicial complex where vertices are the saddle connections on (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\colon \A(S,q) \to \A(S’,q’) between saddle connection complexes is induced by an affine diffeomorphism F \colon (S,q) \to (S’,q’). In particular, this shows that the saddle connection complex is a complete invariant of affine equivalence classes of half-translation surfaces. Throughout our proof, we develop several combinatorial criteria of independent interest for detecting various geometric objects on a half-translation surface.

SEEK ID: https://publications.h-its.org/publications/1001

Research Groups: Groups and Geometry

Publication type: Journal

Journal: arXiV preprints

Citation: arXiV:1810.00961 [math.GT]

Date Published: 2018

URL: https://arxiv.org/abs/1810.00961

Registered Mode: imported from a bibtex file

Authors: Valentina Disarlo, Anja Randecker, Robert Tang

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Views: 5055

Created: 30th Jan 2020 at 10:36

Last updated: 5th Mar 2024 at 21:24

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