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Publication . Article . Other literature type . Preprint . 2009 . Embargo end date: 01 Jan 2006

Triangulated cores of punctured-torus groups

François Guéritaud;
Open Access

doi: 10.48550/arxiv.math/0605481 , 10.4310/jdg/1228400629

Published: 01 Jan 2009
Publisher: arXiv
Abstract

We show that the interior of the convex core of a quasifuchsian punctured-torus group admits an ideal decomposition (usually an infinite triangulation) which is canonical in two different senses: in a combinatorial sense via the pleating invariants, and in a geometric sense via an Epstein-Penner convex hull construction in Minkowski space. The result extends to certain non-quasifuchsian punctured-torus groups, and in fact to all of them if a strong version of the Pleating Lamination Conjecture is true.

Comment: 38 pages, 14 figures

Subjects by Vocabulary

arXiv: Mathematics::Geometric Topology Computer Science::Computational Geometry

Microsoft Academic Graph classification: Combinatorics Conjecture Ideal (set theory) Mathematics Regular polygon Torus Lamination (topology) Convex hull Minkowski space Group (mathematics)

Subjects

Geometric Topology (math.GT), Metric Geometry (math.MG), FOS: Mathematics, 51F99 ; 51H20 ; 52B99 ; 57M50 ; 57M60, Mathematics - Geometric Topology, Mathematics - Metric Geometry, 51F99, 51H20, 52B99, 57M50, 57M60, Geometry and Topology, Algebra and Number Theory, Analysis

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Project Euclid
Other literature type . 2009
Providers: Project Euclid
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