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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Overtwisted open books from sobering arcs

Noah Goodman

Algebraic & Geometric Topology 5 (2005) 1173–1195

arXiv: math.GT/0407420

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.

Keywords
open book, contact structure, overtwisted, sobering arc, symplectic configuration graph
Mathematical Subject Classification 2000
Primary: 57R17
Secondary: 57M99
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Publication
Received: 24 July 2004
Revised: 15 June 2005
Accepted: 26 July 2005
Published: 18 September 2005
Authors
Noah Goodman
Massachusetts Institute of Technology
Cambridge MA 02139
USA