Volume 21, issue 7 (2021)

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

Volume 24
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 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
Turaev hyperbolicity of classical and virtual knots

Colin Adams, Or Eisenberg, Jonah Greenberg, Kabir Kapoor, Zhen Liang, Kate O’Connor, Natalia Pachecho-Tallaj and Yi Wang

Algebraic & Geometric Topology 21 (2021) 3459–3482
Bibliography
1 C Adams, C Albors-Riera, B Haddock, Z Li, D Nishida, B Reinoso, L Wang, Hyperbolicity of links in thickened surfaces, Topology Appl. 256 (2019) 262 MR3916014
2 C Adams, O Eisenberg, J Greenberg, K Kapoor, Z Liang, K O’Connor, N Pacheco-Tallaj, Y Wang, tg-hyperbolicity of virtual links, J. Knot Theory Ramifications 28 (2019) MR4059928
3 C Adams, T Fleming, M Levin, A M Turner, Crossing number of alternating knots in S × I, Pacific J. Math. 203 (2002) 1 MR1895923
4 I Agol, The minimal volume orientable hyperbolic 2–cusped 3–manifolds, Proc. Amer. Math. Soc. 138 (2010) 3723 MR2661571
5 M O Bourgoin, Twisted link theory, Algebr. Geom. Topol. 8 (2008) 1249 MR2443243
6 J S Carter, S Kamada, M Saito, Stable equivalence of knots on surfaces and virtual knot cobordisms, J. Knot Theory Ramifications 11 (2002) 311 MR1905687
7 Y V Drobotukhina, An analogue of the Jones polynomial for links in P3 and a generalization of the Kauffman–Murasugi theorem, Algebra i Analiz 2 (1990) 171 MR1073213
8 A T Fomenko, The theory of invariants of multidimensional integrable Hamiltonian systems (with arbitrary [sic] many degrees of freedom), from: "Topological classification of integrable systems" (editor A T Fomenko), Adv. Soviet Math. 6, Amer. Math. Soc. (1991) 1 MR1141219
9 C M Gordon, J Luecke, Knots are determined by their complements, J. Amer. Math. Soc. 2 (1989) 371 MR965210
10 J A Howie, J S Purcell, Geometry of alternating links on surfaces, Trans. Amer. Math. Soc. 373 (2020) 2349 MR4069222
11 N Kamada, On the Jones polynomials of checkerboard colorable virtual links, Osaka J. Math. 39 (2002) 325 MR1914297
12 N Kamada, S Kamada, Abstract link diagrams and virtual knots, J. Knot Theory Ramifications 9 (2000) 93 MR1749502
13 L H Kauffman, Virtual knot theory, European J. Combin. 20 (1999) 663 MR1721925
14 L H Kauffman, Introduction to virtual knot theory, J. Knot Theory Ramifications 21 (2012) MR2994594
15 G Kuperberg, What is a virtual link?, Algebr. Geom. Topol. 3 (2003) 587 MR1997331
16 V O Manturov, D P Ilyutko, Virtual knots: the state of the art, 51, World Sci. (2013) MR2986036
17 W Menasco, Closed incompressible surfaces in alternating knot and link complements, Topology 23 (1984) 37 MR721450
18 Y Miyamoto, Volumes of hyperbolic manifolds with geodesic boundary, Topology 33 (1994) 613 MR1293303
19 W Thurston, Geometry and topology of three-manifolds, lecture notes (1980)
20 V G Turaev, A simple proof of the Murasugi and Kauffman theorems on alternating links, Enseign. Math. 33 (1987) 203 MR925987
21 O Viro, Virtual links, orientations of chord diagrams and Khovanov homology, from: "Proceedings of Gökova Geometry–Topology Conference" (editors S Akbulut, T Önder, R J Stern), International (2006) 187 MR2282017
22 K Yoshida, The minimal volume orientable hyperbolic 3–manifold with 4 cusps, Pacific J. Math. 266 (2013) 457 MR3130632