13 citations · 26 across the 7 of their papers we have counts for
9 papers · 1 filter
Large-scale geometry of the saddle connection graph
Valentina Disarlo, Huiping Pan, Anja Randecker +1
We prove that the saddle connection graph associated to any half-translation surface is 4-hyperbolic and uniformly quasi-isometric to the regular countably infinite-valent tree. Co…
The model theory of the curve graph
Valentina Disarlo, Thomas Koberda, J. de la Nuez González
In this paper we develop a bridge between model theory, geometric topology, and geometric group theory. In particular, we investigate the Ivanov Metaconjecture from the point of vi…
Generalized stretch lines for surfaces with boundary
Daniele Alessandrini, Valentina Disarlo
In 1986 William P. Thurston introduced the celebrated (asymmetric) Lipschitz distance on the Teichmueller space of a (closed or punctured) surface. In this paper we extend his work…
Rigidity of the saddle connection complex
Valentina Disarlo, Anja Randecker, Robert Tang
For a half-translation surface (S,q), the associated saddle connection complex A(S,q) is the simplicial complex where vertices are the saddle connections on (S,q), with simplices s…
Cubical Geometry in the Polygonalisation Complex
Mark C. Bell, Valentina Disarlo, Robert Tang
We introduce the polygonalisation complex of a surface, a cube complex whose vertices correspond to polygonalisations. This is a geometric model for the mapping class group and it…
Simultaneous flips on triangulated surfaces
Valentina Disarlo, Hugo Parlier
We investigate a type of distance between triangulations on finite type surfaces where one moves between triangulations by performing simultaneous flips. We consider triangulations…
Combinatorial rigidity of arc complexes
Valentina Disarlo
We study the arc complex of a surface with marked points in the interior and on the boundary. We prove that the isomorphism type of the arc complex determines the topology of the u…
The geometry of flip graphs and mapping class groups
Valentina Disarlo, Hugo Parlier
The space of topological decompositions into triangulations of a surface has a natural graph structure where two triangulations share an edge if they are related by a so-called fli…
On the coarse geometry of the complex of domains
Valentina Disarlo
The complex of domains is a geometric tool with a very rich simplicial structure, it contains the curve complex as a simplicial subcomplex. In this paper we shall reg…