Planar open book decompositions and contact structures

Abstract

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.

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

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