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Convex Polytopes and Quasilattices from the Symplectic Viewpoint

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Abstract

We construct, for each convex polytope, possibly nonrational and nonsimple, a family of compact spaces that are stratified by quasifolds, i.e. each of these spaces is a collection of quasifolds glued together in an suitable way. A quasifold is a space locally modelled on \({\mathbb{R}^{k}}\) modulo the action of a discrete, possibly infinite, group. The way strata are glued to each other also involves the action of an (infinite) discrete group. Each stratified space is endowed with a symplectic structure and a moment mapping having the property that its image gives the original polytope back. These spaces may be viewed as a natural generalization of symplectic toric varieties to the nonrational setting.

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Authors and Affiliations

  1. Dipartimento di Matematica Applicata “G. Sansone”, Via S. Marta 3, 50139, Firenze, Italy

    Fiammetta Battaglia

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  1. Fiammetta Battaglia
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Correspondence to Fiammetta Battaglia.

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Communicated by A. Connes

Partially supported by GNSAGA (CNR).

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Battaglia, F. Convex Polytopes and Quasilattices from the Symplectic Viewpoint. Commun. Math. Phys. 269, 283–310 (2007). https://doi.org/10.1007/s00220-006-0130-1

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  • DOI: https://doi.org/10.1007/s00220-006-0130-1

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