Overtwisted open books from sobering arcs

Goodman, Noah

doi:10.2140/agt.2005.5.1173

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Overtwisted open books from sobering arcs

Noah Goodman

Algebraic & Geometric Topology 5 (2005) 1173–1195

DOI: 10.2140/agt.2005.5.1173

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

Volume 5, issue 3 (2005)