Embedded H-holomorphic maps and open book decompositions
Abstract
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.
Cite
@article{arxiv.0907.3939,
title = {Embedded H-holomorphic maps and open book decompositions},
author = {Jens von Bergmann},
journal= {arXiv preprint arXiv:0907.3939},
year = {2009}
}