Algebraic & Geometric Topology

Overtwisted open books from sobering arcs

Noah Goodman

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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.

Article information

Algebr. Geom. Topol., Volume 5, Number 3 (2005), 1173-1195.

Received: 24 July 2004
Revised: 15 June 2005
Accepted: 26 July 2005
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R17: Symplectic and contact topology
Secondary: 57M99: None of the above, but in this section

open book contact structure overtwisted sobering arc symplectic configuration graph


Goodman, Noah. Overtwisted open books from sobering arcs. Algebr. Geom. Topol. 5 (2005), no. 3, 1173--1195. doi:10.2140/agt.2005.5.1173.

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