Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 5, Number 3 (2005), 1173-1195.
Overtwisted open books from sobering arcs
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.
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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Goodman, Noah. Overtwisted open books from sobering arcs. Algebr. Geom. Topol. 5 (2005), no. 3, 1173--1195. doi:10.2140/agt.2005.5.1173. https://projecteuclid.org/euclid.agt/1513796448