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arXiv · 0907.3939

Embedded H-holomorphic maps and open book decompositions

Jens von Bergmann
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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.

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Jens von Bergmann. 2009-07-22. Embedded H-holomorphic maps and open book decompositions. https://arxiv.org/abs/0907.3939

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