Algebraic and Geometric Topology 5 (2005),
paper no. 47, pages 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 in Algebr. Geom. Topol. 3 (2003) 569--586.
Open book, contact structure, overtwisted, sobering arc, symplectic configuration graph
AMS subject classification.
Submitted: 24 July 2004.
(Revised: 15 June 2005.)
Accepted: 26 July 2005.
Published: 18 September 2005.
Notes on file formats
Massachusetts Institute of Technology
Cambridge, MA 02139, USA
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