The Symplectic Geometry of Penrose Rhombus Tilings

Details The Symplectic Geometry of Penrose Rhombus Tilings The Symplectic Geometry of Penrose Rhombus Tilings

2007-11-11

arxiv.org/abs/0711.1642v2

J. Symplectic Geom. 6 (2008), 139-158

Mathematics

Symplectic Geometry

22 pages, 11 figures. Minor improvements. To appear in J. Symplectic Geom

Scientific paper

The purpose of this article is to view Penrose rhombus tilings from the perspective of symplectic geometry. We show that each thick rhombus in such a tiling can be naturally associated to a highly singular 4-dimensional compact symplectic space, while each thin rhombus can be associated to another such space; both spaces are invariant under the Hamiltonian action of a 2-dimensional quasitorus, and the images of the corresponding moment mappings give the rhombuses back. These two spaces are diffeomorphic but not symplectomorphic.

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