Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009. / This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. / Includes bibliographical references (p. 141-145). / Broken Lefschetz fibrations are a new way to depict smooth 4-manifolds and to investigate their topology; for instance, Perutz defines invariants of 4-manifolds by counting J-holomorphic sections of these fibrations. The first part of this thesis is about the calculus of these objects. In particular, based on earlier results we prove the existence of broken Lefschetz fibrations on any smooth oriented closed 4-manifold and describe certain topological manipulations of these objects, to construct new broken Lefschetz fibration, e.g. with better properties from other ones. The second part is about Perutz's invariants for broken Lefschetz fibrations, the corresponding invariants for 3-manifolds mapping to S1, and relating these invariants to Ozsváth-Szabó 3 and 4-manifold invariants. Specifically, we prove an isomorphism between two 3-manifold invariants, namely Perutz's quilted Floer homology and Ozsváth-Szabó Heegaard Floer homology for certain spinc structures. This yields interesting and in a sense simplified geometric interpretations of Ozsváth-Szabó invariants. In particular, we give new calculations of these invariants and other applications, e.g. a proof of Floer's excision theorem in the context of Heegaard Floer homology. / by Yankı Lekili. / Ph.D.
| Identifer | oai:union.ndltd.org:MIT/oai:dspace.mit.edu:1721.1/49881 |
| Date | January 2009 |
| Creators | Lekili, Yankı |
| Contributors | Denis Auroux., Massachusetts Institute of Technology. Dept. of Mathematics., Massachusetts Institute of Technology. Dept. of Mathematics. |
| Publisher | Massachusetts Institute of Technology |
| Source Sets | M.I.T. Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 145 p., application/pdf |
| 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., http://dspace.mit.edu/handle/1721.1/7582 |
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