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arXiv · 0711.1642

The Symplectic Geometry of Penrose Rhombus Tilings

Fiammetta Battaglia·Elisa Prato
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Abstract

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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BibTeXRIS

Fiammetta Battaglia, Elisa Prato. 2008-04-24. The Symplectic Geometry of Penrose Rhombus Tilings. https://arxiv.org/abs/0711.1642

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