87 research outputs found
Contact Dehn surgery, symplectic fillings, and Property P for knots
These are notes of a talk given at the Mathematische Arbeitstagung 2005 in
Bonn. Following ideas of Ozbagci-Stipsicz, a proof based on contact Dehn
surgery is given of Eliashberg's concave filling theorem for contact
3-manifolds. The role of that theorem in the Kronheimer-Mrowka proof of
property P for nontrivial knots is sketched.Comment: 9 page
-plumbings and exotic contact structures on spheres
We prove the existence of exotic but homotopically trivial contact structures
on spheres of dimension 8k-1. Together with previous results of Eliashberg and
the second author this establishes the existence of such structures on all
odd-dimensional spheres (of dimension at least 3).Comment: 12 page
A Legendrian surgery presentation of contact 3-manifolds
We prove that every closed, connected contact 3-manifold can be obtained from
the 3-sphere with its standard contact structure by contact surgery of
coefficient plus or minus 1 along a Legendrian link. As a corollary, we derive
a result of Etnyre and Honda about symplectic cobordisms (in slightly stronger
form).Comment: 18 pages, Section 3 and three figures added. To appear in Math. Proc.
Cambridge Philos. So
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