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Left-orderability and Exceptional Dehn Surgery on Twist Knots

Published online by Cambridge University Press:  20 November 2018

Masakazu Teragaito
Masakazu Teragaito*
Affiliation:
Department of Mathematics and Mathematics Education, Hiroshima University, Higashi-hiroshima, Japan 739-8524 e-mail: teragai@hiroshima-u.ac.jp
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Abstract.

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We show that any exceptional non-trivial Dehn surgery on a twist knot, except the trefoil, yields a 3-manifold whose fundamental group is left-orderable. This is a generalization of a result of Clay, Lidman, and Watson, and also gives a new supporting evidence for a conjecture of Boyer, Gordon, andWatson.

Keywords

57M2506F15left-orderingtwist knotDehn surgery
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 4 , 01 December 2013 , pp. 850 - 859
Copyright
Copyright © Canadian Mathematical Society 2013

References

[1] Bludov, V. V. and Glass, A. M.W., Word problems, embeddings, and free products of right-ordered groups with amalgamated subgroup. Proc. Lond. Math. Soc. (3) 99 (2009), no. 3, 585–608. http://dx.doi.org/10.1112/plms/pdp008 http://dx.doi.org/10.1112/plms/pdp008 Google Scholar
[2] Boyer, S., Gordon, C. McA., and Watson, L., On L-spaces and left-orderable fundamental groups. arxiv:1107.5016.Google Scholar
[3] Boyer, S., Rolfsen, D., and B.Wiest, Orderable 3-manifold groups. Ann. Inst. Fourier (Grenoble) 55 (2005), no. 1, 243–288. http://dx.doi.org/10.5802/aif.2098 Google Scholar
[4] Brittenham, M. and Wu, Y.-Q., The classification of exceptional Dehn surgeries on 2-bridge knots. Comm. Anal. Geom. 9 (2001), no. 1, 97–113.Google Scholar
[5] Burde, G. and Zieschang, H., Knots, de Gruyter Studies in Mathematics, 5, Walter de Gruyter & Co., Berlin, 2003.Google Scholar
[6] Clay, A., Lidman, T., and Watson, L., Graph manifolds, left-orderability and amalgamation. arxiv:1106.0486.Google Scholar
[7] Gabai, D., Foliations and the topology of 3-manifolds. III. J. Differential Geom. 26 (1987), no. 3, 479–536.Google Scholar
[8] Greene, J. E., Alternating links and left-orderability. arxiv:1107.5232.Google Scholar
[9] Ito, T., Non-left-orderable double branched coverings. arxiv:1106.1499.Google Scholar
[10] Navas, A., A remarkable family of left-ordered groups: central extensions of Hecke groups. J. Algebra 328 (2011), 31–42. http://dx.doi.org/10.1016/j.jalgebra.2010.10.020 Google Scholar
[11] Y. Ni, Knot Floer homology detects fibred knots. Invent. Math. 170 (2007), no. 3, 577–608. http://dx.doi.org/10.1007/s00222-007-0075-9 Google Scholar
[12] Ozsváth, P. and Szabö, Z., On knot Floer homology and lens space surgeries. Topology 44 (2005), no. 6, 1281–1300. http://dx.doi.org/10.1016/j.top.2005.05.001 http://dx.doi.org/10.1016/j.top.2005.05.001 Google Scholar