This article is cited in 2 papers

Ammann Tilings in Symplectic Geometry

Fiammetta Battaglia, Elisa Prato

Dipartimento di Matematica e Informatica “U. Dini”, Via S. Marta 3, 50139 Firenze, Italy

Abstract: In this article we study Ammann tilings from the perspective of symplectic geometry. Ammann tilings are nonperiodic tilings that are related to quasicrystals with icosahedral symmetry. We associate to each Ammann tiling two explicitly constructed highly singular symplectic spaces and we show that they are diffeomorphic but not symplectomorphic. These spaces inherit from the tiling its very interesting symmetries.

Keywords: symplectic quasifold; nonperiodic tiling; quasilattice.

MSC: 53D20; 52C23

Received: November 9, 2012; in final form February 27, 2013; Published online March 6, 2013

Language: English

DOI: 10.3842/SIGMA.2013.021

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ArXiv: 1004.2471