We will define the Betti numbers of the generalized toric spaces associated to nonrational simple convex polytopes and show that they depend on the combinatorial type of the polytope exactly as they do in the rational case. We will illustrate this result by focussing on a particular example of simple non rational convex polytope: the Penrose kite.

References

• F. Battaglia, E. Prato, The Symplectic Penrose Kite, Commun. Math. Phys., 299, (2010), Number 3, 577-601.
• F. Battaglia, Betti numbers of the geometric spaces associated to nonrational simple convex polytopes, Proc. Amer. Math. Soc. 139 (2011), 2309-2315.