dc.contributor.advisor | Taubes, Clifford H. | |
dc.contributor.author | Zhang, Boyu | |
dc.date.accessioned | 2019-05-20T12:23:49Z | |
dc.date.created | 2018-05 | |
dc.date.issued | 2018-05-13 | |
dc.date.submitted | 2018 | |
dc.identifier.uri | http://nrs.harvard.edu/urn-3:HUL.InstRepos:40050132 | * |
dc.description.abstract | This thesis studies several compactness problems in gauge theory and explores their applications is low dimensional topology.
The first chapter studies a connection between taut foliations and Seiberg-Witten theory. Let Y be a closed oriented 3-manifold and F a smooth oriented foliation on Y. Assume that F does not admit any transverse invariant measure. This chapter constructs an invariant c(F) for F which takes value in the monopole Floer homology group of Y. The invariant is well defined up to a sign.
The second chapter proves the deformation invariance for the parity of the number of Klein-bottle leaves in a smooth taut foliation. Given two smooth cooriented taut foliations, assume that every Klein-bottle leaf has non-trivial linear holonomy, and assume that the two foliations can be smoothly deformed to each other through taut foliations, then the parities of the number of Klein-bottle leaves are the same.
The third chapter proves that the zero locus of a Z/2 harmonic spinor on a 4 dimensional manifold is 2-rectifiable and has locally finite Minkowski content. | |
dc.description.sponsorship | Mathematics | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en | |
dash.license | LAA | |
dc.subject | Mathematics | |
dc.title | Several Compactness Results in Gauge Theory and Low Dimensional Topology | |
dc.type | Thesis or Dissertation | |
dash.depositing.author | Zhang, Boyu | |
dc.date.available | 2019-05-20T12:23:49Z | |
thesis.degree.date | 2018 | |
thesis.degree.grantor | Graduate School of Arts & Sciences | |
thesis.degree.level | Doctoral | |
thesis.degree.name | Doctor of Philosophy | |
dc.contributor.committeeMember | Kronheimer, Peter B. | |
dc.contributor.committeeMember | Mrowka, Tomasz | |
dc.type.material | text | |
thesis.degree.department | Mathematics | |
dash.identifier.vireo | http://etds.lib.harvard.edu/gsas/admin/view/2316 | |
dc.description.keywords | gauge theory; taut foliations; monopole Floer homology; J-holomorphic curves; Z/2 harmonic spinors | |
dash.author.email | zhangboyu@pku.edu.cn | |