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arXiv · 1205.5118

Tilings of the plane and Thurston semi-norm

J. -R. Chazottes·J. -M. Gambaudo·F. Gautero
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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 $3$-manifolds.

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J. -R. Chazottes, J. -M. Gambaudo, F. Gautero. 2013-11-12. Tilings of the plane and Thurston semi-norm. https://arxiv.org/abs/1205.5118

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