Contact homology of left-handed stabilizations and plumbing of open books

Mathematics – Symplectic Geometry

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

29 pages, 4 figures

Scientific paper

We show that on any closed contact manifold of dimension greater than 1 a contact structure with vanishing contact homology can be constructed. The basic idea for the construction comes from Giroux. We use a special open book decomposition for spheres. The page is the cotangent bundle of a sphere and the monodromy is given by a left-handed Dehn twist. In the resulting contact manifold we exhibit a closed Reeb orbit that bounds a single finite energy plane. As a result, the unit element of the contact homology algebra is exact and so the contact homology vanishes. This result can be extended to other contact manifolds by using connected sums. The latter is related to the plumbing- or 2-Murasugi sum of the contact open books. We shall give a possible description of this construction and some conjectures about the plumbing operation.

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

Contact homology of left-handed stabilizations and plumbing of open books 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 Contact homology of left-handed stabilizations and plumbing of open books, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Contact homology of left-handed stabilizations and plumbing of open books will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-405995

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