Simple Non-Rational Convex Polytopes via Symplectic Geometry

Details Simple Non-Rational Convex Polytopes via Symplectic Geometry Simple Non-Rational Convex Polytopes via Symplectic Geometry

1999-04-30

arxiv.org/abs/math/9904179v2

Topology (40) 2001, 961-975

Mathematics

Symplectic Geometry

latex, 16 pages; revised, references added, to appear in Topology

Scientific paper

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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