Algebraic and Geometric Topology 5 (2005), paper no. 47, pages 1173-1195.

Overtwisted open books from sobering arcs

Noah Goodman

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.

Keywords. Open book, contact structure, overtwisted, sobering arc, symplectic configuration graph

AMS subject classification. Primary: 57R17. Secondary: 57M99.

E-print: arXiv:math/0407420

DOI: 10.2140/agt.2005.5.1173

Submitted: 24 July 2004. (Revised: 15 June 2005.) Accepted: 26 July 2005. Published: 18 September 2005.

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Noah Goodman
Massachusetts Institute of Technology
Cambridge, MA 02139, USA

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