Volume 21, issue 4 (2017)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 29
Issue 2, 549–862
Issue 1, 1–548

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
A characterisation of alternating knot exteriors

Joshua A Howie

Geometry & Topology 21 (2017) 2353–2371
Bibliography
1 C Adams, T Kindred, A classification of spanning surfaces for alternating links, Algebr. Geom. Topol. 13 (2013) 2967 MR3116310
2 R J Aumann, Asphericity of alternating knots, Ann. of Math. 64 (1956) 374 MR0096236
3 C L Curtis, S J Taylor, The Jones polynomial and boundary slopes of alternating knots, J. Knot Theory Ramifications 20 (2011) 1345 MR2851712
4 C H Dowker, M B Thistlethwaite, Classification of knot projections, Topology Appl. 16 (1983) 19 MR702617
5 C M Gordon, Links and their complements, from: "Topology and geometry : commemorating SISTAG" (editors A J Berrick, M C Leung, X Xu), Contemp. Math. 314, Amer. Math. Soc. (2002) 71 MR1941623
6 C M Gordon, J Luecke, Knots are determined by their complements, J. Amer. Math. Soc. 2 (1989) 371 MR965210
7 J E Greene, Alternating links and definite surfaces, preprint (2015) arXiv:1511.06329v1
8 W Haken, Theorie der Normalflächen, Acta Math. 105 (1961) 245 MR0141106
9 A E Hatcher, On the boundary curves of incompressible surfaces, Pacific J. Math. 99 (1982) 373 MR658066
10 J A Howie, Surface-alternating knots and links, PhD thesis, University of Melbourne (2015)
11 J A Howie, J H Rubinstein, Weakly generalised alternating links,
12 W Jaco, J H Rubinstein, 0–efficient triangulations of 3–manifolds, J. Differential Geom. 65 (2003) 61 MR2057531
13 W Jaco, J H Rubinstein, Inflations of ideal triangulations, Adv. Math. 267 (2014) 176 MR3269178
14 W Jaco, E Sedgwick, Decision problems in the space of Dehn fillings, Topology 42 (2003) 845 MR1958532
15 W Jaco, J L Tollefson, Algorithms for the complete decomposition of a closed 3–manifold, Illinois J. Math. 39 (1995) 358 MR1339832
16 W B R Lickorish, An introduction to knot theory, 175, Springer (1997) MR1472978
17 W Menasco, Closed incompressible surfaces in alternating knot and link complements, Topology 23 (1984) 37 MR721450
18 W Menasco, M Thistlethwaite, The classification of alternating links, Ann. of Math. 138 (1993) 113 MR1230928
19 T Nowik, Dissecting the 2–sphere by immersions, Geom. Dedicata 127 (2007) 37 MR2338513
20 C Petronio, Ideal triangulations of link complements and hyperbolicity equations, Geom. Dedicata 66 (1997) 27 MR1454930
21 J H Rubinstein, An algorithm to recognize the 3–sphere, from: "Proceedings of the International Congress of Mathematicians" (editor S D Chatterji), Birkhäuser (1995) 601 MR1403961
22 A Thompson, Thin position and the recognition problem for S3, Math. Res. Lett. 1 (1994) 613 MR1295555