Convex Polytopes and Quasilattices from the Symplectic Viewpoint
Abstract
Description
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 $\R^k$ 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.
LaTeX, 29 pages. Revised version: TITLE changed, reorganization of notations and exposition, added remarks and references
LaTeX, 29 pages. Revised version: TITLE changed, reorganization of notations and exposition, added remarks and references