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arxiv: math/0407420 · v2 · pith:HTVDVDQ4new · submitted 2004-07-24 · 🧮 math.GT · math.SG

Overtwisted open books from sobering arcs

classification 🧮 math.GT math.SG
keywords openovertwistedarcsbookssoberingalgebransweringarising
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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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