Journal of Symplectic Geometry
- J. Symplectic Geom.
- Volume 6, Number 2 (2008), 139-158.
The Symplectic Geometry of Penrose Rhombus Tilings
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.
J. Symplectic Geom., Volume 6, Number 2 (2008), 139-158.
First available in Project Euclid: 27 August 2008
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Battaglia, Fiammetta; Prato, Elisa. The Symplectic Geometry of Penrose Rhombus Tilings. J. Symplectic Geom. 6 (2008), no. 2, 139--158. https://projecteuclid.org/euclid.jsg/1219866510