分野別セミナー

Delzant proves in 1988 that there is a bijective correspondence between symplectic toric manifolds and what are now called Delzant polytopes; so all the geometrical information on a symplectic toric manifold M is encoded by the corresponding Delzant polytope P and the (equivariant) cohomology ring of M is explicitly described in terms of P.

The notion of a toric origami manifold was introduced by Cannas da Silva-Guillemin-Pires in 2010 as a generalization of a symplectic toric manifold, where the 2-form on a toric origami manifold is allowed to degenerate along a hypersurface. They extend the result of Delzant by showing that there is a bijective correspondence between toric origami manifolds and origami templates, where an origami template is a collection of Delzant polytopes satisfying a certain compatibility condition. The topology of toric origami manifolds is rather more complicated than that of symplectic toric manifolds and it is unknown how to describe the (equivariant) cohomology of a toric origami manifold in terms of the associated origami template. In this talk I will overview the topic and explain some development and problems.