19,772 research outputs found
Contact structures on principal circle bundles
We describe a necessary and sufficient condition for a principal circle
bundle over an even-dimensional manifold to carry an invariant contact
structure. As a corollary it is shown that all circle bundles over a given base
manifold carry an invariant contact structure, only provided the trivial bundle
does. In particular, all circle bundles over 4-manifolds admit invariant
contact structures. We also discuss the Bourgeois construction of contact
structures on odd-dimensional tori in this context, and we relate our results
to recent work of Massot, Niederkrueger and Wendl on weak symplectic fillings
in higher dimensions.Comment: 14 pages, 1 figure; v2: changes to exposition, Sections 5.2, 5.3 and
6 are ne
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
-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
- …