Broken Lefschetz fibrations on smooth four-manifolds

dc.contributor.advisorGompf, Robert E., 1957-en
dc.contributor.committeeMemberEtnyre, John B.en
dc.contributor.committeeMemberLuecke, Johnen
dc.contributor.committeeMemberReid, Alanen
dc.contributor.committeeMemberSadun, Lorenzo A.en
dc.creatorWilliams, Jonathan Dunklinen
dc.date.accessioned2010-10-12T20:50:46Zen
dc.date.available2010-10-12T20:50:46Zen
dc.date.available2010-10-12T20:50:51Zen
dc.date.issued2010-05en
dc.date.submittedMay 2010en
dc.date.updated2010-10-12T20:50:52Zen
dc.descriptiontexten
dc.description.abstractIt is known that an arbitrary smooth, oriented four-manifold admits the structure of what is called a broken Lefschetz fibration. Given a broken Lefschetz fibration, there are certain modifications, realized as homotopies of the fibration map, that enable one to construct infinitely many distinct fibrations of the same manifold. The aim of this paper is to prove that these modifications are sufficient to obtain every broken Lefschetz fibration in a given homotopy class of smooth maps. One notable application is that adding an additional projection move generates all broken Lefschetz fibrations, regardless of homotopy class. The paper ends with further applications and open problems.en
dc.description.departmentMathematics
dc.format.mimetypeapplication/pdfen
dc.identifier.urihttp://hdl.handle.net/2152/ETD-UT-2010-05-841en
dc.language.isoengen
dc.subjectManifolden
dc.subject4-manifolden
dc.subjecttopologyen
dc.subjectLefschetzen
dc.subjectfibrationen
dc.subjectBrokenen
dc.subjectSymplecticen
dc.subjectSmoothen
dc.subjectsingularityen
dc.titleBroken Lefschetz fibrations on smooth four-manifoldsen
dc.type.genrethesisen
thesis.degree.departmentMathematicsen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorUniversity of Texas at Austinen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen

Access full-text files

Original bundle

Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
WILLIAMS-DISSERTATION.pdf
Size:
681.68 KB
Format:
Adobe Portable Document Format

License bundle

Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
2.13 KB
Format:
Plain Text
Description: