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Genus one open books with non-left-orderable fundamental group


Authors: Yu Li and Liam Watson
Journal: Proc. Amer. Math. Soc. 142 (2014), 1425-1435
MSC (2010): Primary 57M05, 57M12, 20F60, 06F15
Published electronically: January 10, 2014
MathSciNet review: 3162262
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ Y$ be a closed, connected, orientable three-manifold admitting a genus one open book decomposition with one boundary component. We prove that if $ Y$ is an L-space, then the fundamental group of $ Y$ is not left-orderable. This answers a question posed by John Baldwin.


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Additional Information

Yu Li
Affiliation: School of Mathematics, Nankai University, Tianjin 300071, People’s Republic of China
Address at time of publication: Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, Wisconsin 53706-1325
Email: adterram@math.wisc.edu

Liam Watson
Affiliation: Department of Mathematics, University of California Los Angeles, 520 Portola Plaza, Los Angeles, California 90095
Address at time of publication: School of Mathematics and Statistics, University of Glasgow, 15 University Gardens, Glasgow G12 8QW, United Kingdom
Email: Liam.Watson@glasgow.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-2014-11847-8
Received by editor(s): October 11, 2011
Received by editor(s) in revised form: April 10, 2012, and May 1, 2012
Published electronically: January 10, 2014
Additional Notes: The first author was supported by a CSST undergraduate summer internship
The second author was partially supported by an NSERC postdoctoral fellowship
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2014 American Mathematical Society