Origami manifolds

An origami manifold is a manifold equipped with a closed 2-form which is symplectic everywhere except on a hypersurface, where it is a folded form whose kernel defines a circle fibration. In this thesis I explain how an origami manifold can be unfolded into a collection of symplectic pieces and conversely, how a collection of symplectic pieces can be folded (modulo compatibility conditions) into an origami manifold. Using equivariant versions of these operations, I show how classic symplectic results of convexity and classification of toric manifolds translate to the origami world. Several examples are presented, including a complete classification of toric origami surfaces. Furthermore, I extend the results above to the case of nonorientable origami manifolds.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2010

Author dc:creator

• Pissarra Pires, Ana Rita

Advisor dc:contributor.advisor

• Victor Guillemin.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/60200

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/60200