Algebraic & Geometric Topology Volume 23, issue 4 (2023)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Residual torsion-free nilpotence, biorderability and pretzel knots

Jonathan Johnson

Algebraic & Geometric Topology 23 (2023) 1787–1830

DOI: 10.2140/agt.2023.23.1787

Bibliography

1	G Baumslag, Groups with the same lower central sequence as a relatively free group, I : The groups, Trans. Amer. Math. Soc. 129 (1967) 308 MR217157
2	G Baumslag, Groups with the same lower central sequence as a relatively free group, II : Properties, Trans. Amer. Math. Soc. 142 (1969) 507 MR245653
3	S Boyer, C M Gordon, L Watson, On L-spaces and left-orderable fundamental groups, Math. Ann. 356 (2013) 1213 MR3072799
4	S Boyer, D Rolfsen, B Wiest, Orderable 3–manifold groups, Ann. Inst. Fourier (Grenoble) 55 (2005) 243 MR2141698
5	E M Brown, R H Crowell, The augmentation subgroup of a link, J. Math. Mech. 15 (1966) 1065 MR0196734
6	G Burde, H Zieschang, Neuwirthsche Knoten und Flächenabbildungen, Abh. Math. Sem. Univ. Hamburg 31 (1967) 239 MR229229
7	I M Chiswell, A M W Glass, J S Wilson, Residual nilpotence and ordering in one-relator groups and knot groups, Math. Proc. Cambridge Philos. Soc. 158 (2015) 275 MR3310246
8	A Clay, C Desmarais, P Naylor, Testing bi-orderability of knot groups, Canad. Math. Bull. 59 (2016) 472 MR3563729
9	R H Crowell, H F Trotter, A class of pretzel knots, Duke Math. J. 30 (1963) 373 MR153006
10	D Eisenbud, U Hirsch, W Neumann, Transverse foliations of Seifert bundles and self-homeomorphism of the circle, Comment. Math. Helv. 56 (1981) 638 MR656217
11	D Gabai, The Murasugi sum is a natural geometric operation, II, from: "Combinatorial methods in topology and algebraic geometry" (editors J R Harper, R Mandelbaum), Contemp. Math. 44, Amer. Math. Soc. (1985) 93 MR813105
12	D Gabai, Genera of the arborescent links, 339, Amer. Math. Soc. (1986) MR823442
13	H Goda, M Ishiwata, A classification of Seifert surfaces for some pretzel links, Kobe J. Math. 23 (2006) 11 MR2279856
14	F González-Acuña, Dehn’s construction on knots, Bol. Soc. Mat. Mexicana 15 (1970) 58 MR356022
15	C M Gordon, Ribbon concordance of knots in the 3–sphere, Math. Ann. 257 (1981) 157 MR634459
16	C M Gordon, Riley’s conjecture on SL(2, ℝ) representations of 2–bridge knots, J. Knot Theory Ramifications 26 (2017) 1740003 MR3604485
17	A Issa, H Turner, Links all of whose cyclic branched covers are L-spaces, preprint (2020) arXiv:2008.06127
18	T Ito, Alexander polynomial obstruction of bi-orderability for rationally homologically fibered knot groups, New York J. Math. 23 (2017) 497 MR3649667
19	M Jankins, W D Neumann, Rotation numbers of products of circle homeomorphisms, Math. Ann. 271 (1985) 381 MR787188
20	J Johnson, Residual torsion-free nilpotence, bi-orderability and two-bridge links, Canad. J. Math. (2023)
21	L H Kauffman, State models and the Jones polynomial, Topology 26 (1987) 395 MR899057
22	L H Kauffman, New invariants in the theory of knots, from: "On the geometry of differentiable manifolds", Astérisque 163-164, Soc. Math. France (1988) 137 MR999974
23	A Kawauchi, A survey of knot theory, Birkhäuser (1996) MR1417494
24	W B R Lickorish, M B Thistlethwaite, Some links with nontrivial polynomials and their crossing-numbers, Comment. Math. Helv. 63 (1988) 527 MR966948
25	P A Linnell, A H Rhemtulla, D P O Rolfsen, Invariant group orderings and Galois conjugates, J. Algebra 319 (2008) 4891 MR2423810
26	P Lisca, A I Stipsicz, On the existence of tight contact structures on Seifert fibered 3–manifolds, Duke Math. J. 148 (2009) 175 MR2524494
27	W Magnus, Beziehungen zwischen Gruppen und Idealen in einem speziellen Ring, Math. Ann. 111 (1935) 259 MR1512992
28	W Magnus, A Karrass, D Solitar, Combinatorial group theory: presentations of groups in terms of generators and relations, Interscience (1966) MR0207802
29	E J Mayland Jr., The residual finiteness of the classical knot groups, Canadian J. Math. 27 (1975) 1092 MR387412
30	E J Mayland Jr., K Murasugi, On a structural property of the groups of alternating links, Canadian J. Math. 28 (1976) 568 MR402718
31	J M Montesinos, Surgery on links and double branched covers of S³, from: "Knots, groups, and 3–manifolds (papers dedicated to the memory of R H Fox)" (editor L P Neuwirth), Ann. of Math. Studies 84, Princeton Univ. Press (1975) 227 MR0380802
32	K Murasugi, Jones polynomials and classical conjectures in knot theory, Topology 26 (1987) 187 MR895570
33	K Murasugi, Knot theory and its applications, Birkhäuser (1996) MR1391727
34	R Naimi, Foliations transverse to fibers of Seifert manifolds, Comment. Math. Helv. 69 (1994) 155 MR1259611
35	B Perron, D Rolfsen, On orderability of fibred knot groups, Math. Proc. Cambridge Philos. Soc. 135 (2003) 147 MR1990838
36	D Rolfsen, Knots and links, 7, Publish or Perish (1976) MR0515288
37	J Stallings, On fibering certain 3–manifolds, from: "Topology of 3–manifolds and related topics", Prentice-Hall (1962) 95 MR0158375
38	M B Thistlethwaite, A spanning tree expansion of the Jones polynomial, Topology 26 (1987) 297 MR899051