Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 59, Number 3 (2007), 751-761.
Open books supporting overtwisted contact structures and the Stallings twist
We study open books (or open book decompositions) of a closed oriented 3-manifold which support overtwisted contact structures. We focus on a simple closed curve along which one can perform Stallings twist, called "twisting loop". We show that the existence of a twisting loop on the fiber surface of an open book is equivalent up to positive stabilization to the existence of an overtwisted disk in the contact manifold supported by the open book. We also show a criterion for overtwistedness using a certain arc properly embedded in the fiber surface, which is an extension of Goodman's one.
J. Math. Soc. Japan, Volume 59, Number 3 (2007), 751-761.
First available in Project Euclid: 5 October 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
YAMAMOTO, Ryosuke. Open books supporting overtwisted contact structures and the Stallings twist. J. Math. Soc. Japan 59 (2007), no. 3, 751--761. doi:10.2969/jmsj/05930751. https://projecteuclid.org/euclid.jmsj/1191591856