Princeton-Rider Workshop Abstracts
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چکیده
Toric origami manifold is a generalization of a symplectic toric manifold: it is a manifold with torus action and a compatible 2-form degenerating in a nice, controllable way. In the same way as symplectic toric manifolds are classified by Delzant polytopes, symplectic toric manifolds are classified by certain collections of Delzant polytopes, called origami templates. We are interested in the following question: are there quasitoric manifolds which are not toric origami? It happens that in dimension 6 there are plenty of them: we introduce a certain parameter of a polytope: the fatness, and show that fat polytopes admit a quasitoric manifold which is not toric origami. To show that there exist fat polytopes one can use an isoperimetric inequality on a sphere. Moreover, some recent developments in the theory of large random planar maps show that most simple 3-polytopes are fat. This means, that most simple 3-polytopes admit a quasitoric manifold which is not toric origami. This is a joint work with M.Masuda, S.Park and H.Zeng.
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