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5 Publications visible to you, out of a total of 5
Large-scale geometry of the saddle connection graph

Abstract

Not specified

Authors: Valentina Disarlo, Huiping Pan, Anja Randecker, Robert Tang

Date Published: 1st Nov 2021

Publication Type: Journal

Generalizing Stretch Lines for Surfaces with Boundary

Abstract

Not specified

Authors: Daniele Alessandrini, Valentina Disarlo

Date Published: 8th Sep 2021

Publication Type: Journal

Generalized stretch lines for surfaces with boundary

Abstract (Expand)

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 to the Teichmueller … space of a surface with boundary endowed the arc distance. In this new setting we construct a large family of geodesics, which generalize Thurston’s stretch lines. We prove that the Teichmueller space of a surface with boundary, endowed with the arc distance, is a geodesic metric space. Furthermore, the arc distance is induced by a Finsler metric. As a corollary, we describe a new class of geodesics in the Teichmueller space of a closed/punctured surface that are not stretch lines in the sense of Thurston.

Authors: Daniele Alessandrini, Valentina Disarlo

Date Published: 2019

Publication Type: Misc

Simultaneous ips on triangulated surfaces

Abstract (Expand)

We investigate a type of distance between triangulations on finite-type surfaces where one moves between triangulations by performing simultaneous flips. We consider triangulations up to homeomorphism, … and our main results are upper bounds on the distance between triangulations that only depend on the topology of the surface.

Authors: Valentina Disarlo, Hugo Parlier

Date Published: 1st Aug 2018

Publication Type: Journal

Rigidity of the saddle connection complex

Abstract (Expand)

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 …s 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.

Authors: Valentina Disarlo, Anja Randecker, Robert Tang

Date Published: 2018

Publication Type: Journal

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