Origami manifolds
Name
681966912-MIT.pdf
Description
Full printable version
Size
3.97 MB
Format
Adobe PDF
Checksum (MD5)
a3aafe4b9e0a60181b17c1cdb775434a
Author(s)
Pissarra Pires, Ana Rita
Advisor(s)
Victor Guillemin.
Date Issued
2010
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 51).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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copyright. They may be viewed from this source for any purpose, but
reproduction or distribution in any format is prohibited without written
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