Symplectic Origami

Details Symplectic Origami Symplectic Origami

2009-09-22

arxiv.org/abs/0909.4065v2

Mathematics

Symplectic Geometry

v2; 42 pages, 18 figures; significant revision; to appear in Int. Math. Res. Not.; first published online December 2, 2010

Scientific paper

10.1093/imrn/rnq241

An origami manifold is a manifold equipped with a closed 2-form which is symplectic except on a hypersurface where it is like the pullback of a symplectic form by a folding map and its kernel fibrates with oriented circle fibers over a compact base. We can move back and forth between origami and symplectic manifolds using cutting (unfolding) and radial blow-up (folding), modulo compatibility conditions. We prove an origami convexity theorem for hamiltonian torus actions, classify toric origami manifolds by polyhedral objects resembling paper origami and discuss examples. We also prove a cobordism result and compute the cohomology of a special class of origami manifolds.

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