2026-09-20T11:56:33Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1221652026-06-16T18:52:30Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Emmy Murphy.
Sackel, Kevin(Kevin Ryan)
Massachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2019-09-16T22:33:47Z
2019-09-16T22:33:47Z
2019
2019
https://hdl.handle.net/1721.1/122165
1117775056
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2019
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 141-143).
In this thesis, we develop the details of a surgery theory for contact manifolds of arbitrary dimension via convex structures, extending the 3-dimensional theory developed by Giroux. The theory is analogous to that of Weinstein manifolds in symplectic geometry, with the key difference that the vector field does not necessarily have positive divergence everywhere. The surgery theory for contact manifolds contains the surgery theory for Weinstein manifolds via a sutured model for attaching critical points of low index. Using this sutured model, we show that the existence of convex structures on closed contact manifolds is guaranteed, a result equivalent to the existence of supporting Weinstein open book decompositions. In the final chapter, we provide a few words about how this theory is related to the Giroux correspondence between Weinstein open book decompositions and contact structures in three dimensions, as well as providing a framework for possible generalizations to higher dimensions and homotopy data.
by Kevin Sackel.
Ph.D.
Ph.D. Massachusetts Institute of Technology, Department of Mathematics
143 pages
eng
Massachusetts Institute of Technology
MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.
http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Getting a handle on contact manifolds
Thesis
application/pdf
2019-09-16T22:33:47Z
Publication
Doctoral
Math
unknown
unknown
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