Geodesic
Testing Bi-orderability of Knot Groups
Canadian mathematical bulletin, Tome 59 (2016) no. 3, pp. 472-482

Voir la notice de l'article provenant de la source Cambridge University Press

We investigate the bi-orderability of two-bridge knot groups and the groups of knots with 12 or fewer crossings by applying recent theorems of Chiswell, Glass and Wilson. Amongst all knots with 12 or fewer crossings (of which there are 2977), previous theorems were only able to determine bi-orderability of 499 of the corresponding knot groups. With our methods we are able to deal with 191 more.
DOI : 10.4153/CMB-2016-023-6
Mots-clés : 57M25, 57M27, 06F15, knots, fundamental groups, orderable groups 
Clay, Adam; Desmarais, Colin; Naylor, Patrick. Testing Bi-orderability of Knot Groups. Canadian mathematical bulletin, Tome 59 (2016) no. 3, pp. 472-482. doi: 10.4153/CMB-2016-023-6
@article{10_4153_CMB_2016_023_6,
     author = {Clay, Adam and Desmarais, Colin and Naylor, Patrick},
     title = {Testing {Bi-orderability} of {Knot} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {472--482},
     year = {2016},
     volume = {59},
     number = {3},
     doi = {10.4153/CMB-2016-023-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-023-6/}
}
TY  - JOUR
AU  - Clay, Adam
AU  - Desmarais, Colin
AU  - Naylor, Patrick
TI  - Testing Bi-orderability of Knot Groups
JO  - Canadian mathematical bulletin
PY  - 2016
SP  - 472
EP  - 482
VL  - 59
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-023-6/
DO  - 10.4153/CMB-2016-023-6
ID  - 10_4153_CMB_2016_023_6
ER  - 
%0 Journal Article
%A Clay, Adam
%A Desmarais, Colin
%A Naylor, Patrick
%T Testing Bi-orderability of Knot Groups
%J Canadian mathematical bulletin
%D 2016
%P 472-482
%V 59
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-023-6/
%R 10.4153/CMB-2016-023-6
%F 10_4153_CMB_2016_023_6

[1] [1] Akhmedovand, A. Martin, C., Non-bi-orderability of 62 and76- arxiv:abs/1512.00372. Google Scholar

[2] [2] Boyer, S., Rolfsen, D., and Wiest, B., Orderable 3-manifold groups. Ann. Institut Fourier (Grenoble) 55(2005), 243–288. Google Scholar | DOI

[3] [3] Boyer, S., Gordon, C. M., and Watson, L., On L-spaces and left-orderable fundamental groups. Math. Ann. 356(2013), no. 4, 1213–1245. Google Scholar | DOI

[4] [4] Cha, J. C. and Livingston, C., Knotinfo: Table of knot invariants, Http://Www.Indiana.Edu/Knotinfo. Google Scholar

[5] [5] Chiswell, I. M., Glass, A. M. W., and Wilson, J. S., Residual nilpotence and ordering in one-relator groups and knot groups. Math. Proc. Cambridge Philos. Soc. 158(2015), no. 2, 275–288. Google Scholar | DOI

[6] [6] Clay, A. and Rolfsen, D., Ordered groups, eigenvalues, knots, surgery and L-spaces. Math.Proc. Cambridge Philos. Soc. 152(2012), no. 1,115-129. Google Scholar | DOI

[7] [7] Culler, M., Dunfield, N. M., and Weeks, J. R., SnapPy, a computer program for studying the topology ofi-manifolds. http://snappy.computop.org Google Scholar

[8] [8] Dorrie, H., 100 great problems of elementary mathematics: their history and solution. Dover, New York, 1965. Google Scholar

[9] [9] Hoste, J. and Shanahan, P. D., Twisted Alexander polynomials of2-bridge knots. J. Knot Theory Ramifications 22(2013), no. 1, 1250138, 29. Google Scholar | DOI

[10] [10] Ito, T.. A remark on the Alexander polynomial criterion for the bi-orderabilityoffibered 3-manifold groups. Int. Math. Res. Not. IMRN (1):156-169, 2013. Google Scholar

[11] [11] Linnell, P. A., Rhemtulla, A. H., and Rolfsen, D. P. O., Invariant group orderings and Galois conjugates. J. Algebra 319(2008), no. 12, 4891–4898. Google Scholar | DOI

[12] [12] Lyndon, R. C. and Schupp, P. E., Combinatorial group theory. Ergebnisse der Mathematik und ihrerGrenzgebiete 89, Springer-Verlag, Berlin, 1977. Google Scholar

[13] [13] Murasugi, K., Remarks on knots with two bridges. Proc. Japan Acad. 37(1961), 294–297. Google Scholar | DOI

[14] [14] Naylor, G. and Rolfsen, D., Generalized torsion in knot groups. Canad.Math. Bull. 59(2016), no. 1, 182–189. Google Scholar | DOI

[15] [15] Perron, B. and Rolfsen, D., On orderability of fibred knot groups. Math. Proc. Cambridge Philos. Soc. 135(2003), no. 1, 147–153. Google Scholar | DOI

[16] [16] Perron, B. and Rolfsen, D., Invariant ordering of surface groups and 3-manifolds which fibre over S'.Math. Proc. Cambridge Philos. Soc. 141(2006), no. 2, 273–280. Google Scholar | DOI

[17] [17] Saveliev, N., Lectures on the topology ofS-manifolds. deGruyter Textbook. Walter de Gruyter, Berlin, 1999. Google Scholar

[18] [18] Schubert, H., Knotenmit zweiBrucken. Math. Z. 65(1956), 133–170. Google Scholar | DOI

Cité par Sources :