English

Symplectic Origami

Symplectic Geometry 2016-11-03 v2

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.

Keywords

Cite

@article{arxiv.0909.4065,
  title  = {Symplectic Origami},
  author = {A. Cannas da Silva and V. Guillemin and A. R. Pires},
  journal= {arXiv preprint arXiv:0909.4065},
  year   = {2016}
}

Comments

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

R2 v1 2026-06-21T13:49:14.765Z