Overtwisted open books from sobering arcs

Noah Goodman

doi:10.2140/agt.2005.5.1173

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Home > Journals > Algebr. Geom. Topol. > Volume 5 > Issue 3 > Article

2005 Overtwisted open books from sobering arcs

Noah Goodman

Algebr. Geom. Topol. 5(3): 1173-1195 (2005). DOI: 10.2140/agt.2005.5.1173

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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.