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arXiv · 0909.4065

Symplectic Origami

A. Cannas da Silva·V. Guillemin·A. R. Pires
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Abstract

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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A. Cannas da Silva, V. Guillemin, A. R. Pires. 2011-02-21. Symplectic Origami. https://doi.org/10.1093/imrn%2Frnq241

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