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Overtwisted open books from sobering arcs

Noah Goodman
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Abstract

We study open books on three manifolds which are compatible with an overtwisted contact structure. We show that the existence of certain arcs, called sobering arcs, is a sufficient condition for an open book to be overtwisted, and is necessary up to stabilization by positive Hopf-bands. Using these techniques we prove that some open books arising as the boundary of symplectic configurations are overtwisted, answering a question of Gay in Algebr. Geom. Topol. 3 (2003) 569--586.

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BibTeXRIS

Noah Goodman. 2005-10-11. Overtwisted open books from sobering arcs. https://doi.org/10.2140/agt.2005.5.1173

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