Simple Non-Rational Convex Polytopes via Symplectic Geometry
Symplectic Geometry
2010-04-23 v2 Differential Geometry
Geometric Topology
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.
Cite
@article{arxiv.math/9904179,
title = {Simple Non-Rational Convex Polytopes via Symplectic Geometry},
author = {Elisa Prato},
journal= {arXiv preprint arXiv:math/9904179},
year = {2010}
}
Comments
latex, 16 pages; revised, references added, to appear in Topology