Genus one open books with non-left-orderable fundamental group
HTML articles powered by AMS MathViewer
- by Yu Li and Liam Watson PDF
- Proc. Amer. Math. Soc. 142 (2014), 1425-1435 Request permission
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.References
- John A. Baldwin, Heegaard Floer homology and genus one, one-boundary component open books, J. Topol. 1 (2008), no. 4, 963–992. MR 2461862, DOI 10.1112/jtopol/jtn029
- Steven Boyer, Cameron McA. Gordon, and Liam Watson, On L-spaces and left-orderable fundamental groups, Math. Ann. 356 (2013), no. 4, 1213–1245. MR 3072799, DOI 10.1007/s00208-012-0852-7
- Steven Boyer, Dale Rolfsen, and Bert Wiest, Orderable 3-manifold groups, Ann. Inst. Fourier (Grenoble) 55 (2005), no. 1, 243–288 (English, with English and French summaries). MR 2141698
- Adam Clay and Liam Watson, Left-orderable fundamental groups and Dehn surgery, Int. Math. Res. Not. IMRN 12 (2013), 2862–2890. MR 3071667, DOI 10.1093/imrn/rns129
- Adam Clay and Liam Watson, On cabled knots, Dehn surgery, and left-orderable fundamental groups, Math. Res. Lett. 18 (2011), no. 6, 1085–1095. MR 2915469, DOI 10.4310/MRL.2011.v18.n6.a4
- Joshua Evan Greene, A spanning tree model for the Heegaard Floer homology of a branched double-cover, J. Topol. 6 (2013), no. 2, 525–567. MR 3065184, DOI 10.1112/jtopol/jtt007
- —, Alternating links and left-orderability, preprint, arXiv:1107.5232.
- Tetsuya Ito, Non-left-orderable double branched coverings, Algebr. Geom. Topol. 13 (2013), no. 4, 1937–1965. MR 3073904, DOI 10.2140/agt.2013.13.1937
- Kunio Murasugi, On closed $3$-braids, Memoirs of the American Mathematical Society, No. 151, American Mathematical Society, Providence, R.I., 1974. MR 0356023
- Peter Ozsváth and Zoltán Szabó, On knot Floer homology and lens space surgeries, Topology 44 (2005), no. 6, 1281–1300. MR 2168576, DOI 10.1016/j.top.2005.05.001
- Peter Ozsváth and Zoltán Szabó, On the Heegaard Floer homology of branched double-covers, Adv. Math. 194 (2005), no. 1, 1–33. MR 2141852, DOI 10.1016/j.aim.2004.05.008
- Thomas Peters, On L-spaces and non left-orderable 3-manifold groups, preprint, arXiv:0903.4495.
- Peter Scott, The geometries of $3$-manifolds, Bull. London Math. Soc. 15 (1983), no. 5, 401–487. MR 705527, DOI 10.1112/blms/15.5.401
- Liam Watson, A surgical perspective on quasi-alternating links, Low-dimensional and symplectic topology, Proc. Sympos. Pure Math., vol. 82, Amer. Math. Soc., Providence, RI, 2011, pp. 39–51. MR 2768652, DOI 10.1090/pspum/082/2768652
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
- 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
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 142 (2014), 1425-1435
- MSC (2010): Primary 57M05, 57M12, 20F60, 06F15
- DOI: https://doi.org/10.1090/S0002-9939-2014-11847-8
- MathSciNet review: 3162262