Tilings of the plane and Thurston semi-norm

Jean René Chazottes; Jean Marc Gambaudo; François Gautero

doi:10.1007/s10711-013-9932-4

Tilings of the plane and Thurston semi-norm

Jean René Chazottes
, Jean Marc Gambaudo
, François Gautero

Université Côte D’Azur
Université de Nice

Research output: Contribution to journal › Article › peer-review

Abstract

We show that the problem of tiling the Euclidean plane with a finite set of polygons (up to translation) boils down to prove the existence of zeros of a non-negative convex function defined on a finite-dimensional simplex. This function is a generalisation, in the framework of branched surfaces, of the Thurston semi-norm originally defined for compact $$3$$3-manifolds.

Original language	English
Pages (from-to)	129-142
Number of pages	14
Journal	Geometriae Dedicata
Volume	173
Issue number	1
DOIs	https://doi.org/10.1007/s10711-013-9932-4
Publication status	Published - 1 Dec 2014

Keywords

Branched surfaces
Euclidean tilings
Translation surfaces

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10.1007/s10711-013-9932-4

Cite this

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title = "Tilings of the plane and Thurston semi-norm",

abstract = "We show that the problem of tiling the Euclidean plane with a finite set of polygons (up to translation) boils down to prove the existence of zeros of a non-negative convex function defined on a finite-dimensional simplex. This function is a generalisation, in the framework of branched surfaces, of the Thurston semi-norm originally defined for compact \$\$3\$\$3-manifolds.",

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AB - We show that the problem of tiling the Euclidean plane with a finite set of polygons (up to translation) boils down to prove the existence of zeros of a non-negative convex function defined on a finite-dimensional simplex. This function is a generalisation, in the framework of branched surfaces, of the Thurston semi-norm originally defined for compact $$3$$3-manifolds.

KW - Branched surfaces

KW - Euclidean tilings

KW - Translation surfaces

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Tilings of the plane and Thurston semi-norm

Abstract

Keywords

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