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Non-Right-Orderable 3-Manifold Groups

Published online by Cambridge University Press:  20 November 2018

R. Roberts
Affiliation:
Department of Mathematics, Washington University, St Louis, MO 63130 e-mail: roberts@math.wustl.edushareshi@math.wustl.edu
J. Shareshian
Affiliation:
Department of Mathematics, Washington University, St Louis, MO 63130 e-mail: roberts@math.wustl.edushareshi@math.wustl.edu
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Abstract

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We exhibit infinitely many hyperbolic 3-manifold groups that are not right-orderable.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2010

References

[BH96] Bleiler, S. and Hodgson, C. D., Spherical space forms and Dehn filling. Topology 35(1996), no. 3, 809833. doi:10.1016/0040-9383(95)00040-2Google Scholar
[BRW02] Boyer, S., Rolfsen, D., and Wiest, B., Orderable 3-manifold groups. Ann. Inst. Fourier (Grenoble) 55(2005), no. 1, 243288.Google Scholar
[CaCo99] Candel, A. and Conlon, L., Foliations. I. Graduate Studies in Mathematics, 23, American Mathematical Society, Providence, RI, 2000.Google Scholar
[CJR84] Culler, M., Jaco, W., and Rubenstein, H., Incompressible surfaces in once-punctured torus bundles. Proc. London Math. Soc. (3) 45(1982), no. 3, 385419. doi:10.1112/plms/s3-45.3.385Google Scholar
[DPT05] Da¸bkowski, M. K., Przytycki, J. H., and Togha, A. A., Non-left-orderable 3-manifold groups. Canad. Math. Bull. 48(2005), no. 1, 3240.Google Scholar
[Fen07] Fenley, S., Laminar free hyperbolic 3-manifolds. Comment. Math. Helv. 82(2007), no. 2, 247321. doi:10.4171/CMH/92Google Scholar
[Fen94] Fenley, S. R., Anosov flows in 3-manifolds. Ann. of Math. (2) 139(1994), no. 1, 79115. doi:10.2307/2946628Google Scholar
[FH82] Floyd, W. and Hatcher, A., Incompressible surfaces in punctured-torus bundles. Topology Appl. 13(1982), no. 3, 263282. doi:10.1016/0166-8641(82)90035-9Google Scholar
[Ha92] Hatcher, A., Some examples of essential laminations in 3-manifolds. Ann. Inst. Fourier (Grenoble) 42(1992), no. 1–2, 313332.Google Scholar
[Ind06] Indurskis, G., Fillings of one boundary component of the Whitehead link. Ph.D. thesis, Université du Québec à Montréal, 2006.Google Scholar
[Li99] Linnell, P. A., Left ordered amenable and locally indicable groups. J. London Math. Soc. (2) 60(1999), no. 1, 133142. doi:10.1112/S0024610799007462Google Scholar
[Ni17] Nielsen, J., Die Isomorphismen der allgemeinen unendlichen Gruppe mit zwei Erzeugenden. Math. Ann. 78(1964), no. 1, 385397. doi:10.1007/BF01457113Google Scholar
[Pl83] Plante, J. F., Solvable groups acting on the line. Trans. Amer. Math. Soc. 278(1983), no. 1, 401414. doi:10.2307/1999325Google Scholar
[RSS03] Roberts, R., Shareshian, J., and Stein, M., Infinitely many hyperbolic 3-manifolds which contain no Reebless foliation. J. Amer. Math. Soc. 16(2003), no. 3, 639679. doi:10.1090/S0894-0347-03-00426-0Google Scholar
[Rol90] Rolfsen, D., Knots and links. Mathematics Lecture Series, 7, Publish or Perish, Inc., Houston, TX, 1990.Google Scholar
[Th79] Thurston, W., The geometry and topology of three-manifolds, Princeton, 1979. http://www.msri.org/publications/books/gt3m Google Scholar