Planar open book decompositions and contact structures

Details Planar open book decompositions and contact structures Planar open book decompositions and contact structures

2004-04-14

arxiv.org/abs/math/0404267v3

Mathematics

Symplectic Geometry

10 pages, 3 figures. Proof that overtwisted contact structures are supported by open books is corrected. Various improvements

Scientific paper

In this note we observe that while all overtwisted contact structures on
compact 3--manifolds are supported by planar open book decompositions, not all
contact structures are. This has relevance to invariants of contact structures
and also to the Weinstein conjecture via work of Abbas Cieliebak and Hofer.

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