|
Geometry & Topology 13 (2009)
623–660
|
| 1 |
J W Alexander,
Topological
invariants of knots and links, Trans. Amer. Math. Soc.
30 (1928) 275–306 MR1501429 |
| 2 |
D Bar-Natan,
On
the Vassiliev knot invariants, Topology 34 (1995)
423–472 MR1318886 |
| 3 |
D Bar-Natan,
Khovanov's homology
for tangles and cobordisms, Geom. Topol. 9 (2005)
1443–1499 MR2174270 |
| 4 |
J S Birman,
X S Lin, Knot polynomials and
Vassiliev's invariants, Invent. Math. 111 (1993)
225–270 MR1198809 |
| 5 |
G Burde, H
Zieschang, Knots, de Gruyter Studies in Mathematics
5, Walter de Gruyter & Co. (1985) MR808776 |
| 6 |
A J Casson,
C M Gordon, Cobordism of classical knots,
from: "À la recherche de la topologie perdue", Progr.
Math. 62, Birkhäuser (1986) 181–199 MR900252
With an appendix by P M Gilmer |
| 7 |
T D Cochran,
Concordance
invariance of coefficients of Conway's link polynomial,
Invent. Math. 82 (1985) 527–541 MR811549 |
| 8 |
J H Conway, An
enumeration of knots and links, and some of their algebraic
properties, from: "Computational Problems in Abstract
Algebra (Proc. Conf., Oxford, 1967)", Pergamon (1970)
329–358 MR0258014 |
| 9 |
M Eisermann,
A
geometric characterization of Vassiliev invariants,
Trans. Amer. Math. Soc. 355 (2003) 4825–4846 MR1997586 |
| 10 |
M Eisermann, Finite
type invariants of surfaces in 3–space, in
preparation (2008) |
| 11 |
M Eisermann, C
Lamm, A refined Jones polynomial for symmetric
unions (2008) arXiv:0802.2283 |
| 12 |
D Erle, Quadratische
Formen als Invarianten von Einbettungen der Kodimension
2, Topology 8 (1969) 99–114 MR0238300 |
| 13 |
V Florens, On the
Fox–Milnor theorem for the Alexander polynomial of
links, Int. Math. Res. Not. (2004) 55–67 MR2040323 |
| 14 |
R H Fox, Some
problems in knot theory, from: "Topology of
3–manifolds and related topics (Proc. The Univ. of
Georgia Institute, 1961)", Prentice-Hall (1962) 168–176
MR0140100 |
| 15 |
R H Fox,
J W Milnor, Singularities
of 2–spheres in 4–space and cobordism of
knots, Osaka J. Math. 3 (1966) 257–267 MR0211392 |
| 16 |
P Freyd, D
Yetter, J Hoste, W B R Lickorish,
K Millett, A Ocneanu, A new
polynomial invariant of knots and links, Bull. Amer.
Math. Soc. (N.S.) 12 (1985) 239–246 MR776477 |
| 17 |
S Garoufalidis,
Signatures of links and finite type invariants of cyclic
branched covers, from: "Tel Aviv Topology Conference:
Rothenberg Festschrift (1998)", Contemp. Math. 231, Amer. Math.
Soc. (1999) 87–97 MR1705577 |
| 18 |
C M Gordon,
Ribbon
concordance of knots in the 3–sphere, Math. Ann.
257 (1981) 157–170 MR634459 |
| 19 |
M N Gusarov, A
new form of the Conway–Jones polynomial of oriented
links, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst.
Steklov. (LOMI) 193 (1991) 4–9 MR1157140
English translation in [47] |
| 20 |
M Jacobsson,
An
invariant of link cobordisms from Khovanov homology,
Algebr. Geom. Topol. 4 (2004) 1211–1251 MR2113903 |
| 21 |
V F R Jones,
A
polynomial invariant for knots via von Neumann
algebras, Bull. Amer. Math. Soc. (N.S.) 12 (1985)
103–111 MR766964 |
| 22 |
L H Kauffman,
On knots, Annals of Mathematics Studies 115, Princeton
University Press (1987) MR907872 |
| 23 |
L H Kauffman,
State models
and the Jones polynomial, Topology 26 (1987)
395–407 MR899057 |
| 24 |
L H Kauffman,
An invariant of
regular isotopy, Trans. Amer. Math. Soc. 318 (1990)
417–471 MR958895 |
| 25 |
A Kawauchi,
On the Alexander polynomials of cobordant links, Osaka
J. Math. 15 (1978) 151–159 MR0488022 |
| 26 |
M Khovanov,
A
categorification of the Jones polynomial, Duke Math. J.
101 (2000) 359–426 MR1740682 |
| 27 |
M Khovanov,
An
invariant of tangle cobordisms, Trans. Amer. Math. Soc.
358 (2006) 315–327 MR2171235 |
| 28 |
R Kirby,
editor, Problems in
low-dimensional topology, from: "Geometric topology
(Athens, GA, 1993)", AMS/IP Stud. Adv. Math. 2 (1997) MR1470751 |
| 29 |
S Lang,
Algebra, Graduate Texts in Mathematics 211, Springer
(2002) MR1878556 |
| 30 |
C Lescop, Global
surgery formula for the Casson–Walker invariant,
Annals of Mathematics Studies 140, Princeton University Press
(1996) MR1372947 |
| 31 |
J Levine, Knot cobordism groups in
codimension two, Comment. Math. Helv. 44 (1969)
229–244 MR0246314 |
| 32 |
W B R
Lickorish, An introduction to knot theory, Graduate
Texts in Mathematics 175, Springer (1997) MR1472978 |
| 33 |
C Livingston, A
survey of classical knot concordance, from: "Handbook of
knot theory", Elsevier B. V., Amsterdam (2005) 319–347
MR2179265 |
| 34 |
J W Milnor,
Infinite cyclic coverings, from: "Conference on the
Topology of Manifolds (Michigan State Univ., E. Lansing, Mich.,
1967)", Prindle, Weber & Schmidt, Boston (1968)
115–133 MR0242163 |
| 35 |
Y Mizuma, Ribbon
knots of 1–fusion, the Jones polynomial, and the
Casson–Walker invariant, Rev. Mat. Complut. 18 (2005)
387–425 MR2166517
With an appendix by Tsuyoshi Sakai |
| 36 |
Y Mizuma, An
estimate of the ribbon number by the Jones polynomial,
Osaka J. Math. 43 (2006) 365–369 MR2262340 |
| 37 |
D Mullins, The
generalized Casson invariant for 2–fold branched covers
of S3 and the Jones polynomial, Topology 32
(1993) 419–438 MR1217078 |
| 38 |
H Murakami, T
Ohtsuki, Finite type invariants of knots via their
Seifert matrices, Asian J. Math. 5 (2001) 379–386
MR1868640 |
| 39 |
H Murakami, T
Ohtsuki, S Yamada, Homfly polynomial via an
invariant of colored plane graphs, Enseign. Math. (2) 44
(1998) 325–360 MR1659228 |
| 40 |
K Murasugi,
On a certain
numerical invariant of link types, Trans. Amer. Math.
Soc. 117 (1965) 387–422 MR0171275 |
| 41 |
G Polya, Induction
and analogy in mathematics. Mathematics and plausible
reasoning, vol. I, Princeton University Press (1954) |
| 42 |
J H Przytycki,
P Traczyk, Invariants of links of Conway type,
Kobe J. Math. 4 (1988) 115–139 MR945888 |
| 43 |
J A Rasmussen,
Khovanov homology and the slice genus, Invent. Math. (to
appear) arXiv:math/0402131 |
| 44 |
D Rolfsen, Knots
and links, Mathematics Lecture Series 7, Publish or Perish
(1990) MR1277811
Corrected reprint of the 1976 original |
| 45 |
A G Tristram,
Some cobordism invariants for links, Proc. Cambridge
Philos. Soc. 66 (1969) 251–264 MR0248854 |
| 46 |
V A Vassiliev,
Cohomology of knot spaces, from: "Theory of
singularities and its applications", Adv. Soviet Math. 1, Amer.
Math. Soc. (1990) 23–69 MR1089670 |
| 47 |
O Viro, editor,
Topology of manifolds and varieties, Advances in Soviet
Mathematics 18, Amer. Math. Soc. (1994) |
