Title:
On embeddings of 3-manifolds in symplectic 4-manifolds
On embeddings of 3-manifolds in symplectic 4-manifolds
dc.contributor.advisor | Etnyre, John B. | |
dc.contributor.author | Mukherjee, Anubhav | |
dc.contributor.committeeMember | Hom, Jennifer | |
dc.contributor.committeeMember | Margalit, Dan | |
dc.contributor.committeeMember | Manolescu, Ciprian | |
dc.contributor.committeeMember | Ozsvath, Peter | |
dc.contributor.department | Mathematics | |
dc.date.accessioned | 2022-08-25T13:35:06Z | |
dc.date.available | 2022-08-25T13:35:06Z | |
dc.date.created | 2022-08 | |
dc.date.issued | 2022-07-13 | |
dc.date.submitted | August 2022 | |
dc.date.updated | 2022-08-25T13:35:06Z | |
dc.description.abstract | We proposed a conjecture that every 3-manifolds smoothly embedded in some closed symplectic 4-manifolds. This work shows that any closed oriented 3-manifold can be topologically embedded in some simply-connected closed symplectic 4-manifold, and that it can be made a smooth embedding after one stabilization. As a corollary of the proof we show that the homology cobordism group is generated by Stein fillable 3-manifolds. We also find obstructions on smooth embeddings: there exists 3-manifolds which cannot smoothly embed in a way that appropriately respect orientations in any symplectic manifold with weakly convex boundary. | |
dc.description.degree | Ph.D. | |
dc.format.mimetype | application/pdf | |
dc.identifier.uri | http://hdl.handle.net/1853/67241 | |
dc.language.iso | en_US | |
dc.publisher | Georgia Institute of Technology | |
dc.subject | symplectic geometry, contact geometry, Kirby calculus | |
dc.title | On embeddings of 3-manifolds in symplectic 4-manifolds | |
dc.type | Text | |
dc.type.genre | Dissertation | |
dspace.entity.type | Publication | |
local.contributor.advisor | Etnyre, John B. | |
local.contributor.corporatename | College of Sciences | |
local.contributor.corporatename | School of Mathematics | |
relation.isAdvisorOfPublication | a9264768-2f0a-4f64-842d-cff98031262b | |
relation.isOrgUnitOfPublication | 85042be6-2d68-4e07-b384-e1f908fae48a | |
relation.isOrgUnitOfPublication | 84e5d930-8c17-4e24-96cc-63f5ab63da69 | |
thesis.degree.level | Doctoral |