English

Tilings of the plane and Thurston semi-norm

Metric Geometry 2014-07-08 v2 Geometric Topology

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 33-manifolds.

Keywords

Cite

@article{arxiv.1205.5118,
  title  = {Tilings of the plane and Thurston semi-norm},
  author = {J. -R. Chazottes and J. -M. Gambaudo and F. Gautero},
  journal= {arXiv preprint arXiv:1205.5118},
  year   = {2014}
}

Comments

14 pages, 5 figures. To appear in Geometria Dedicata