Four-dimensional symplectic cobordisms containing three-handles

Mathematics – Geometric Topology

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

This is the version published by Geometry & Topology on 28 October 2006

Scientific paper

10.2140/gt.2006.10.1749

We construct four-dimensional symplectic cobordisms between contact three-manifolds generalizing an example of Eliashberg. One key feature is that any handlebody decomposition of one of these cobordisms must involve three-handles. The other key feature is that these cobordisms contain chains of symplectically embedded two-spheres of square zero. This, together with standard gauge theory, is used to show that any contact three-manifold of non-zero torsion (in the sense of Giroux) cannot be strongly symplectically fillable. John Etnyre pointed out to the author that the same argument together with compactness results for pseudo-holomorphic curves implies that any contact three-manifold of non-zero torsion satisfies the Weinstein conjecture. We also get examples of weakly symplectically fillable contact three-manifolds which are (strongly) symplectically cobordant to overtwisted contact three-manifolds, shedding new light on the structure of the set of contact three-manifolds equipped with the strong symplectic cobordism partial order.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Four-dimensional symplectic cobordisms containing three-handles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Four-dimensional symplectic cobordisms containing three-handles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Four-dimensional symplectic cobordisms containing three-handles will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-390330

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.