Contact structures and open books
| dc.contributor.advisor | Gompf, Robert E., 1957- | en |
| dc.creator | Goodman, Noah Daniel | en |
| dc.date.accessioned | 2008-08-28T21:28:21Z | en |
| dc.date.available | 2008-08-28T21:28:21Z | en |
| dc.date.issued | 2003 | en |
| dc.description | text | en |
| dc.description.abstract | We explore the correspondence between open books and contact structures on three-manifolds. We begin with the necessary definitions and proofs for the correspondence; then we obtain technical results to understand the relationship between compatibility, Murasugi sum, and homotopy classes of plane fields. We use these to prove Harer’s conjecture on fibered links. Finally we explore the topological meaning of overtwistedness. We define sobering arcs in an open book and give a condition, then a criterion, for an open book to be overtwisted. Using this condition we give examples of overtwisted open books which come from positive configuration graphs. Finally we explore the limits of our sobering arc technique. | |
| dc.description.department | Mathematics | en |
| dc.format.medium | electronic | en |
| dc.identifier | b5680863x | en |
| dc.identifier.oclc | 56087867 | en |
| dc.identifier.proqst | 3116314 | en |
| dc.identifier.uri | http://hdl.handle.net/2152/609 | en |
| dc.language.iso | eng | en |
| dc.rights | Copyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works. | en |
| dc.subject.lcsh | Three-manifolds (Topology) | en |
| dc.title | Contact structures and open books | en |
| dc.type.genre | Thesis | en |
| thesis.degree.department | Mathematics | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | The University of Texas at Austin | en |
| thesis.degree.level | Doctoral | en |
| thesis.degree.name | Doctor of Philosophy | en |