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 M_R, while each thin rhombus can be associated to another such space M_r; 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. The spaces M_R and M_r are diffeomorphic but not symplectomorphic.
The Symplectic Geometry of Penrose Rhombus Tilings / F.Battaglia; E.Prato. - In: JOURNAL OF SYMPLECTIC GEOMETRY. - ISSN 1527-5256. - STAMPA. - 6:(2008), pp. 139-158. [10.4310/JSG.2008.v6.n2.a2]
The Symplectic Geometry of Penrose Rhombus Tilings
BATTAGLIA, FIAMMETTA;PRATO, ELISA
2008
Abstract
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 M_R, while each thin rhombus can be associated to another such space M_r; 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. The spaces M_R and M_r are diffeomorphic but not symplectomorphic.File | Dimensione | Formato | |
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symplectic_rhombi.pdf
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