Surgery diagrams for contact 3-manifolds
| dc.creator | Ding, Fan | |
| dc.creator | Geiges, Hansjörg | |
| dc.creator | Stipsicz, András I. | |
| dc.date | 2003-07-17 | |
| dc.date.accessioned | 2026-07-07T04:59:43Z | |
| dc.date.available | 2026-07-07T04:59:43Z | |
| dc.description | In two previous papers, the two first-named authors introduced a notion of contact r-surgery along Legendrian knots in contact 3-manifolds. They also showed how (at least in principle) to convert any contact r-surgery into a sequence of contact plus or minus 1 surgeries, and used this to prove that any (closed) contact 3-manifold can be obtained from the standard contact structure on the 3-sphere by a sequence of such surgeries. In the present paper, we give a shorter proof of that result and a more explicit algorithm for turning a contact r-surgery into plus or minus 1 surgeries. We use this to give explicit surgery diagrams for all contact structures on the 3-sphere and S^1\times S^2, as well as all overtwisted contact structures on arbitrary closed, orientable 3-manifolds. This amounts to a new proof of the Lutz-Martinet theorem that each homotopy class of 2-plane fields on such a manifold is represented by a contact structure. | |
| dc.description | 32 pages, 14 figures | |
| dc.identifier | https://arxiv.org/abs/math/0307237 | |
| dc.identifier | http://arxiv.org/abs/math/0307237 | |
| dc.identifier | Turkish J. Math. 28 (2004), 41-74 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68101 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Geometric Topology | |
| dc.subject | 53D35; 57M25, 57R65 | |
| dc.title | Surgery diagrams for contact 3-manifolds | |
| dc.type | text |