Surgery diagrams for contact 3-manifolds

dc.creatorDing, Fan
dc.creatorGeiges, Hansjörg
dc.creatorStipsicz, András I.
dc.date2003-07-17
dc.date.accessioned2026-07-07T04:59:43Z
dc.date.available2026-07-07T04:59:43Z
dc.descriptionIn 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.description32 pages, 14 figures
dc.identifierhttps://arxiv.org/abs/math/0307237
dc.identifierhttp://arxiv.org/abs/math/0307237
dc.identifierTurkish J. Math. 28 (2004), 41-74
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68101
dc.subjectSymplectic Geometry
dc.subjectGeometric Topology
dc.subject53D35; 57M25, 57R65
dc.titleSurgery diagrams for contact 3-manifolds
dc.typetext

Files

Collections