Embedded H-holomorphic maps and open book decompositions

Details Embedded H-holomorphic maps and open book decompositions Embedded H-holomorphic maps and open book decompositions

2009-07-22

arxiv.org/abs/0907.3939v1

Mathematics

Symplectic Geometry

Scientific paper

We investigate nicely embedded H--holomorphic maps into stable Hamiltonian three--manifolds. In particular we prove that such maps locally foliate and satisfy a no--first--intersection property. Using the compactness results of arXiv:0904.1603 we show that connected components of the space of such maps can be compactified if they contain a global surface of section. As an application we prove that any contact structure on a 3--manifold admits and H--holomorphic open book decomposition. This work is motivated by the program laid out by Abbas, Cieliebak and Hofer to give a proof to the Weinstein conjecture using holomorphic curves. The results in this paper, with the exception of the compactness statement, have been independently obtained by C. Abbas in arXiv:0907.3512.

Affiliated with

Also associated with

No associations

Rating

Embedded H-holomorphic maps and open book decompositions 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 Embedded H-holomorphic maps and open book decompositions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Embedded H-holomorphic maps and open book decompositions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-354218