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

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

Access to Document

10.1007/s10711-013-9932-4

Cite this

@article{101e61d2bc6640ebbd04a08ffa2467d2,

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.",

keywords = "Branched surfaces, Euclidean tilings, Translation surfaces",

author = "Chazottes, \{Jean Ren{\'e}\} and Gambaudo, \{Jean Marc\} and Fran{\c c}ois Gautero",

note = "Publisher Copyright: {\textcopyright} 2014, Springer Science+Business Media Dordrecht.",

year = "2014",

month = dec,

day = "1",

doi = "10.1007/s10711-013-9932-4",

language = "English",

volume = "173",

pages = "129--142",

journal = "Geometriae Dedicata",

issn = "0046-5755",

number = "1",

}

TY - JOUR

T1 - Tilings of the plane and Thurston semi-norm

AU - Chazottes, Jean René

AU - Gambaudo, Jean Marc

AU - Gautero, François

PY - 2014/12/1

Y1 - 2014/12/1

N2 - 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.

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

U2 - 10.1007/s10711-013-9932-4

DO - 10.1007/s10711-013-9932-4

M3 - Article

AN - SCOPUS:84892945237

SN - 0046-5755

VL - 173

SP - 129

EP - 142

JO - Geometriae Dedicata

JF - Geometriae Dedicata

IS - 1

ER -

Tilings of the plane and Thurston semi-norm

Abstract

Keywords

Access to Document

Fingerprint

Cite this