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Simple Non-Rational Convex Polytopes via Symplectic Geometry

Elisa Prato
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Abstract

In this article we consider a generalization of manifolds and orbifolds which we call quasifolds; quasifolds of dimension k are locally isomorphic to the quotient of R^k by the action of a discrete group - tipically they are not Hausdorff topological spaces. The analogue of a torus in this geometry is a quasitorus. We define Hamiltonian actions of quasitori on symplectic quasifolds and we show that any simple convex polytope, rational or not, is the image of the moment mapping for a family of effective Hamiltonian actions on symplectic quasifolds having twice the dimension of the corresponding quasitorus.

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Elisa Prato. 2000-02-04. Simple Non-Rational Convex Polytopes via Symplectic Geometry. https://arxiv.org/abs/math/9904179

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