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Straightening cell decompositions of cusped hyperbolic 3-manifolds

Marina Pescini (1998)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let M be an oriented cusped hyperbolic 3-manifold and let τ be a topological ideal triangulation of M . We give a characterization for τ to be isotopic to an ideal geodesic triangulation; moreover we give a characterization for τ to flatten into a partially flat triangulation. Finally we prove that straightening combinatorially equivalent topological ideal cell decompositions gives the same geodesic decomposition, up to isometry.

Strong surjectivity of maps from 2-complexes into the 2-sphere

Marcio Fenille, Oziride Neto (2010)

Open Mathematics

Given a model 2-complex K P of a group presentation P, we associate to it an integer matrix ΔP and we prove that a cellular map f: K P → S 2 is root free (is not strongly surjective) if and only if the diophantine linear system ΔP Y = d e g (f) has an integer solution, here d e g (f)is the so-called vector-degree of f

Structure of geodesics in the Cayley graph of infinite Coxeter groups

Ryszard Szwarc (2003)

Colloquium Mathematicae

Let (W,S) be a Coxeter system such that no two generators in S commute. Assume that the Cayley graph of (W,S) does not contain adjacent hexagons. Then for any two vertices x and y in the Cayley graph of W and any number k ≤ d = dist(x,y) there are at most two vertices z such that dist(x,z) = k and dist(z,y) = d - k. Allowing adjacent hexagons, but assuming that no three hexagons can be adjacent to each other, we show that the number of such intermediate vertices at a given distance from x and y...

Structures affines et projectives sur les surfaces complexes

Bruno Klingler (1998)

Annales de l'institut Fourier

Une structure complexe affine (resp. projective) sur une surface complexe est la donnée d’un atlas de cartes à valeur dans 2 (resp. P 2 ) à changements de cartes localement constants dans le groupe affine A ( 2 , ) (resp. le groupe P G L ( 3 , ) ). Dans cet article nous classifions les surfaces complexes affines et calculons, à surface complexe S fixée, l’espace de déformation des structures complexes affines sur S compatibles avec sa structure analytique. Nous montrons aussi que toute structure projective sur une surface...

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