Volume 5, issue 2 (2005)

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

Volume 19
Issue 4, 1619–2150
Issue 3, 1079–1618
Issue 2, 533–1078
Issue 1, 1–532

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
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Other MSP Journals
Minimal surface representations of virtual knots and links

H A Dye and Louis H Kauffman

Algebraic & Geometric Topology 5 (2005) 509–535
Bibliography
1 G E Bredon, Topology and geometry, Graduate Texts in Mathematics 139, Springer (1997) MR1700700
2 A Bartholomew, R Fenn, Quaternionic invariants of virtual knots and links, J. Knot Theory Ramifications 17 (2008) 231 MR2398735
3 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
4 H A Dye, Virtual knots undetected by 1– and 2–strand bracket polynomials, Topology Appl. 153 (2005) 141 MR2172041
5 R Fenn, C Rourke, B Sanderson, The rack space, Trans. Amer. Math. Soc. 359 (2007) 701 MR2255194
6 M W Hirsch, Differential topology, Graduate Texts in Mathematics 33, Springer (1994) MR1336822
7 N Kamada, S Kamada, Abstract link diagrams and virtual knots, J. Knot Theory Ramifications 9 (2000) 93 MR1749502
8 L H Kauffman, Detecting virtual knots, Atti Sem. Mat. Fis. Univ. Modena 49 (2001) 241 MR1881100
9 L H Kauffman, Virtual knot theory, European J. Combin. 20 (1999) 663 MR1721925
10 L H Kauffman, S L Lins, Temperley–Lieb recoupling theory and invariants of 3–manifolds, Annals of Mathematics Studies 134, Princeton University Press (1994) MR1280463
11 L H Kauffman, V O Manturov, Virtual biquandles, Fund. Math. 188 (2005) 103 MR2191942
12 L K Kaufman, V O Manturov, Virtual knots and links, Tr. Mat. Inst. Steklova 252 (2006) 114 MR2255973
13 T Kishino, S Satoh, A note on non-classical virtual knots, J. Knot Theory Ramifications 13 (2004) 845 MR2101229
14 T Kadokami, Detecting non-triviality of virtual links, J. Knot Theory Ramifications 12 (2003) 781 MR2008880
15 G Kuperberg, What is a virtual link?, Algebr. Geom. Topol. 3 (2003) 587 MR1997331
16 G Kuperberg, private conversation
17 V O Manturov, Multi-variable polynomial invariants for virtual links, J. Knot Theory Ramifications 12 (2003) 1131 MR2017985
18 S Matveev, Algorithmic topology and classification of 3–manifolds, Algorithms and Computation in Mathematics 9, Springer (2003) MR1997069
19 S Eliahou, L H Kauffman, M B Thistlethwaite, Infinite families of links with trivial Jones polynomial, Topology 42 (2003) 155 MR1928648
20 V V Prasolov, A B Sossinsky, Knots, links, braids and 3–manifolds, Translations of Mathematical Monographs 154, American Mathematical Society (1997) MR1414898
21 D S Silver, S G Williams, On a class of virtual knots with unit Jones polynomial, J. Knot Theory Ramifications 13 (2004) 367 MR2061174
22 V F R Jones, The annular structure of subfactors, from: "Essays on geometry and related topics, Vol. 1, 2", Monogr. Enseign. Math. 38, Enseignement Math. (2001) 401 MR1929335
23 V F R Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. $(2)$ 126 (1987) 335 MR908150