Broken Lefschetz fibrations, Lagrangian matching invariants and Ozsváth-Szabó invariants

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2009

Author dc:creator

• Lekili, Yankı

Advisor dc:contributor.advisor

• Denis Auroux.

• 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/1721.1/49881

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/49881