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arxiv: 1205.5118 · v2 · pith:SSNMCG6Rnew · submitted 2012-05-23 · 🧮 math.MG · math.GT

Tilings of the plane and Thurston semi-norm

J.-R. Chazottes , J.-M. Gambaudo , F. Gautero This is my paper
classification 🧮 math.MG math.GT
keywords definedfunctionplanesemi-normthurstonboilsbranchedcompact
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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 $3$-manifolds.

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