Getting a handle on contact manifolds
Name
1117775056-MIT.pdf
Size
8.91 MB
Format
Adobe PDF
Checksum (MD5)
5644748315a1ea8e4f0dce291188f483
Author(s)
Sackel, Kevin(Kevin Ryan)
Advisor(s)
Emmy Murphy.
Date Issued
2019
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2019
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 141-143).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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