Recent Issues
Volume 24, 8 issues
Volume 24
Issue 8, 4139–4730
Issue 7, 3571–4137
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 23
Issue 9, 3909–4400
Issue 8, 3417–3908
Issue 7, 2925–3415
Issue 6, 2415–2924
Issue 5, 1935–2414
Issue 4, 1463–1934
Issue 3, 963–1462
Issue 2, 509–962
Issue 1, 1–508
Volume 22, 8 issues
Volume 22
Issue 8, 3533–4008
Issue 7, 3059–3532
Issue 6, 2533–3057
Issue 5, 2007–2532
Issue 4, 1497–2006
Issue 3, 991–1495
Issue 2, 473–990
Issue 1, 1–472
Volume 21, 7 issues
Volume 21
Issue 7, 3221–3734
Issue 6, 2677–3220
Issue 5, 2141–2676
Issue 4, 1595–2140
Issue 3, 1075–1593
Issue 2, 543–1074
Issue 1, 1–541
Volume 20, 7 issues
Volume 20
Issue 7, 3219–3760
Issue 6, 2687–3218
Issue 5, 2145–2685
Issue 4, 1601–2143
Issue 3, 1073–1600
Issue 2, 531–1072
Issue 1, 1–529
Volume 19, 7 issues
Volume 19
Issue 7, 3217–3753
Issue 6, 2677–3215
Issue 5, 2151–2676
Issue 4, 1619–2150
Issue 3, 1079–1618
Issue 2, 533–1078
Issue 1, 1–532
Volume 18, 7 issues
Volume 18
Issue 7, 3749–4373
Issue 6, 3133–3747
Issue 5, 2509–3131
Issue 4, 1883–2507
Issue 3, 1259–1881
Issue 2, 635–1258
Issue 1, 1–633
Volume 17, 6 issues
Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643
Volume 16, 6 issues
Volume 16
Issue 6, 3073–3719
Issue 5, 2459–3071
Issue 4, 1827–2458
Issue 3, 1253–1825
Issue 2, 621–1251
Issue 1, 1–620
Volume 15, 6 issues
Volume 15
Issue 6, 3107–3729
Issue 5, 2479–3106
Issue 4, 1863–2477
Issue 3, 1239–1862
Issue 2, 623–1238
Issue 1, 1–622
Volume 14, 6 issues
Volume 14
Issue 6, 3141–3763
Issue 5, 2511–3139
Issue 4, 1881–2509
Issue 3, 1249–1879
Issue 2, 627–1247
Issue 1, 1–625
Volume 13, 6 issues
Volume 13
Issue 6, 3099–3731
Issue 5, 2471–3097
Issue 4, 1857–2469
Issue 3, 1243–1856
Issue 2, 625–1241
Issue 1, 1–624
Volume 12, 4 issues
Volume 12
Issue 4, 1901–2517
Issue 3, 1265–1899
Issue 2, 643–1263
Issue 1, 1–641
Volume 11, 5 issues
Volume 11
Issue 5, 2477–3084
Issue 4, 1861–2475
Issue 3, 1243–1860
Issue 2, 625–1242
Issue 1, 1–624
Volume 10, 4 issues
Volume 10
Issue 4, 1865–2468
Issue 3, 1245–1863
Issue 2, 627–1244
Issue 1, 1–625
Volume 9, 4 issues
Volume 9
Issue 4, 1885–2502
Issue 3, 1255–1883
Issue 2, 625–1254
Issue 1, 1–624
Volume 8, 4 issues
Volume 8
Issue 4, 1855–2414
Issue 3, 1223–1853
Issue 2, 615–1222
Issue 1, 1–613
Volume 7, 4 issues
Volume 7
Issue 4, 1633–2270
Issue 3, 1135–1632
Issue 2, 529–1134
Issue 1, 1–528
Volume 6, 5 issues
Volume 6
Issue 5, 2031–2518
Issue 4, 1519–2029
Issue 3, 1025–1517
Issue 2, 513–1024
Issue 1, 1–512
Volume 5, 4 issues
Volume 5
Issue 4, 1291–1732
Issue 3, 865–1290
Issue 2, 443–864
Issue 1, 1–442
Volume 4, 2 issues
Volume 4
Issue 2, 647–1272
Issue 1, 1–645
Volume 3, 2 issues
Volume 3
Issue 2, 623–1292
Issue 1, 1–622
Volume 2, 2 issues
Volume 2
Issue 2, 591–1204
Issue 1, 1–590
Volume 1, 2 issues
Volume 1
Issue 2, 627–790
Issue 1, 1–625
1
B Audoux , P
Bellingeri , J B Meilhan , E Wagner ,
Homotopy
classification of ribbon tubes and welded string links ,
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 17 (2017) 713 MR3700382
2
D Bar-Natan ,
Vassiliev homotopy
string link invariants , J. Knot Theory Ramifications 4
(1995) 13 MR1321289
3
D Bar-Natan ,
Crossing
the crossings , lecture (2015)
4
V G Bardakov ,
P Bellingeri , Groups of virtual
and welded links , J. Knot Theory Ramifications 23
(2014) MR3200494
5
H U Boden , M
Chrisman , Virtual concordance
and the generalized Alexander polynomial , J. Knot
Theory Ramifications 30 (2021) MR4284604
6
H U Boden , M
Chrisman , R Gaudreau , Virtual knot
cobordism and bounding the slice genus , Exp. Math. 28
(2019) 475 MR4032961
7
H U Boden , M
Chrisman , R Gaudreau , Signature and
concordance of virtual knots , Indiana Univ. Math. J. 69
(2020) 2395 MR4195608
8
H U Boden , E
Dies , A I Gaudreau , A Gerlings , E
Harper , A J Nicas , Alexander
invariants for virtual knots , J. Knot Theory
Ramifications 24 (2015) MR3342135
9
H U Boden , R
Gaudreau , E Harper , A J Nicas , L
White , Virtual knot groups and
almost classical knots , Fund. Math. 238 (2017) 101
MR3640614
10
H U Boden , M
Nagel , Concordance group of
virtual knots , Proc. Amer. Math. Soc. 145 (2017) 5451
MR3717970
11
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
12
K T Chen ,
R H Fox , R C Lyndon , Free differential calculus,
IV : The quotient groups of the lower central series ,
Ann. of Math. (2) 68 (1958) 81
MR102539
13
Z Cheng , H Gao ,
A
polynomial invariant of virtual links , J. Knot Theory
Ramifications 22 (2013) MR3149308
14
M Chrisman ,
Band-passes
and long virtual knot concordance , J. Knot Theory
Ramifications 26 (2017) MR3692566
15
D Cimasoni , V
Turaev , A
generalization of several classical invariants of
links , Osaka J. Math. 44 (2007) 531 MR2360939
16
T D Cochran ,
Derivatives of
links : Milnor’s concordance invariants and Massey’s
products , 427, Amer. Math. Soc. (1990) MR1042041
17
T D Cochran ,
K E Orr , Not all links are concordant
to boundary links , Ann. of Math. (2) 138 (1993) 519 MR1247992
18
T D Cochran ,
K E Orr , P Teichner , Knot concordance,
Whitney towers and L 2 –signatures , Ann. of Math.
(2) 157 (2003) 433 MR1973052
19
A S Crans , A
Henrich , S Nelson , Polynomial knot and
link invariants from the virtual biquandle , J. Knot
Theory Ramifications 22 (2013) MR3055555
20
H A Dye , A
Kaestner , L H Kauffman , Khovanov homology,
Lee homology and a Rasmussen invariant for virtual
knots , J. Knot Theory Ramifications 26 (2017) MR3627701
21
H A Dye ,
L H Kauffman , Virtual
homotopy , J. Knot Theory Ramifications 19 (2010) 935
MR2673693
22
R A Fenn ,
Techniques of geometric topology , 57, Cambridge Univ.
Press (1983) MR787801
23
T G Group ,
GAP: groups,
algorithms, and programming , software (2019)
24
J Green , A table of
virtual knots , electronic resource (2004)
25
N Habegger ,
X S Lin , The classification of links
up to link-homotopy , J. Amer. Math. Soc. 3 (1990) 389
MR1026062
26
N Habegger ,
X S Lin , On link concordance
and Milnor’s μ invariants , Bull. Lond. Math.
Soc. 30 (1998) 419 MR1620841
27
N Habegger , G
Masbaum , The Kontsevich
integral and Milnor’s invariants , Topology 39 (2000)
1253 MR1783857
28
M Hall Jr. , The
theory of groups , Macmillan (1959) MR0103215
29
A Henrich , A sequence of
degree one Vassiliev invariants for virtual knots , J.
Knot Theory Ramifications 19 (2010) 461 MR2646641
30
J A Hillman ,
Alexander
ideals and Chen groups , Bull. Lond. Math. Soc. 10
(1978) 105 MR478132
31
F Jaeger , L H
Kauffman , H Saleur , The Conway polynomial
in ℝ 3 and in thickened surfaces : a new
determinant formulation , J. Combin. Theory Ser. B 61
(1994) 237 MR1280610
32
H Karimi , The Khovanov homology
of alternating virtual links , Michigan Math. J. 70
(2021) 749 MR4332676
33
L H Kauffman ,
Virtual
knot theory , European J. Combin. 20 (1999) 663 MR1721925
34
L H Kauffman ,
A self-linking
invariant of virtual knots , Fund. Math. 184 (2004) 135
MR2128048
35
L H Kauffman ,
An
affine index polynomial invariant of virtual knots , J.
Knot Theory Ramifications 22 (2013) MR3055558
36
L H Kauffman ,
Virtual knot
cobordism , from: "New ideas in low dimensional
topology" (editors L H Kauffman, V O Manturov), Ser.
Knots Everything 56, World Sci. (2015) 335 MR3381329
37
L H Kauffman ,
D Radford , Bi-oriented quantum
algebras, and a generalized Alexander polynomial for virtual
links , from: "Diagrammatic morphisms and applications"
(editors D E Radford, F J O Souza, D N
Yetter), Contemp. Math. 318, Amer. Math. Soc. (2003) 113
MR1973514
38
G Kuperberg ,
What is a
virtual link? , Algebr. Geom. Topol. 3 (2003) 587
MR1997331
39
X S Lin ,
Power
series expansions and invariants of links , from:
"Geometric topology" (editor W H Kazez), AMS/IP Stud. Adv.
Math. 2, Amer. Math. Soc. (1997) 184 MR1470727
40
W Magnus , A
Karrass , D Solitar , Combinatorial group theory:
presentations of groups in terms of generators and
relations , Interscience (1966) MR0207802
41
V O Manturov ,
On
invariants of virtual links , Acta Appl. Math. 72 (2002)
295 MR1916950
42
V O Manturov ,
Compact and long virtual knots , Tr. Mosk. Mat. Obs. 69
(2008) 5 MR2549444
43
B Mellor , Alexander and
writhe polynomials for virtual knots , J. Knot Theory
Ramifications 25 (2016) MR3530309
44
J Milnor , Isotopy of
links , from: "Algebraic geometry and topology : a
symposium in honor of S Lefschetz" (editors R H Fox,
D C Spencer, A W Tucker), Princeton Math. Ser. 12,
Princeton Univ. Press (1957) 280 MR0092150
45
K Y Ng ,
Groups of
ribbon knots , Topology 37 (1998) 441 MR1489214
46
W Nickel , Computing
nilpotent quotients of finitely presented groups , from:
"Geometric and computational perspectives on infinite groups"
(editors G Baumslag, D Epstein, R Gilman, H Short, C Sims),
DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 25, Amer.
Math. Soc. (1996) 175 MR1364184
47
K E Orr ,
Homotopy
invariants of links , Invent. Math. 95 (1989) 379
MR974908
48
M Polyak , Minimal generating sets of
Reidemeister moves , Quantum Topol. 1 (2010) 399
MR2733246
49
D Roseman , Reidemeister-type moves for
surfaces in four-dimensional space , from: "Knot theory"
(editors V F R Jones, J Kania-Bartoszyńska, J H
Przytycki, P Traczyk, V G Turaev), Banach Center Publ. 42,
Polish Acad. Sci. Inst. Math. (1998) 347 MR1634466
50
W Rushworth ,
Computations of
the slice genus of virtual knots , Topology Appl. 253
(2019) 57 MR3892369
51
S Satoh , Virtual knot
presentation of ribbon torus-knots , J. Knot Theory
Ramifications 9 (2000) 531 MR1758871
52
J Sawollek , On
Alexander–Conway polynomials for virtual knots and links ,
preprint (1999) arXiv:math/9912173
53
D S Silver ,
S G Williams , Virtual knot
groups , from: "Knots in Hellas ’98" (editors C M
Gordon, V F R Jones, L H Kauffman, S
Lambropoulou, J H Przytycki), Ser. Knots Everything 24,
World Sci. (2000) 440 MR1865722
54
D S Silver ,
S G Williams , Alexander groups
and virtual links , J. Knot Theory Ramifications 10
(2001) 151 MR1822148
55
D S Silver ,
S G Williams , Polynomial
invariants of virtual links , J. Knot Theory
Ramifications 12 (2003) 987 MR2017967
56
D S Silver ,
S G Williams , Crowell’s derived
group and twisted polynomials , J. Knot Theory
Ramifications 15 (2006) 1079 MR2275098
57
J Stallings ,
Homology and
central series of groups , J. Algebra 2 (1965) 170
MR175956
58
L Traldi , Milnor’s invariants and the
completions of link modules , Trans. Amer. Math. Soc.
284 (1984) 401 MR742432
59
V Turaev , Cobordism of knots on
surfaces , J. Topol. 1 (2008) 285 MR2399131