Volume 13, issue 2 (2009)

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

Volume 26
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

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 Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
The Jones polynomial of ribbon links

Michael Eisermann

Geometry & Topology 13 (2009) 623–660
Bibliography
1 J W Alexander, Topological invariants of knots and links, Trans. Amer. Math. Soc. 30 (1928) 275 MR1501429
2 D Bar-Natan, On the Vassiliev knot invariants, Topology 34 (1995) 423 MR1318886
3 D Bar-Natan, Khovanov's homology for tangles and cobordisms, Geom. Topol. 9 (2005) 1443 MR2174270
4 J S Birman, X S Lin, Knot polynomials and Vassiliev's invariants, Invent. Math. 111 (1993) 225 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 MR900252
7 T D Cochran, Concordance invariance of coefficients of Conway's link polynomial, Invent. Math. 82 (1985) 527 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 MR0258014
9 M Eisermann, A geometric characterization of Vassiliev invariants, Trans. Amer. Math. Soc. 355 (2003) 4825 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 MR0238300
13 V Florens, On the Fox–Milnor theorem for the Alexander polynomial of links, Int. Math. Res. Not. (2004) 55 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 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 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 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 MR1705577
18 C M Gordon, Ribbon concordance of knots in the $3$–sphere, Math. Ann. 257 (1981) 157 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, 161 MR1157140
20 M Jacobsson, An invariant of link cobordisms from Khovanov homology, Algebr. Geom. Topol. 4 (2004) 1211 MR2113903
21 V F R Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. $($N.S.$)$ 12 (1985) 103 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 MR899057
24 L H Kauffman, An invariant of regular isotopy, Trans. Amer. Math. Soc. 318 (1990) 417 MR958895
25 A Kawauchi, On the Alexander polynomials of cobordant links, Osaka J. Math. 15 (1978) 151 MR0488022
26 M Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000) 359 MR1740682
27 M Khovanov, An invariant of tangle cobordisms, Trans. Amer. Math. Soc. 358 (2006) 315 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 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 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 MR0242163
35 Y Mizuma, Ribbon knots of 1–fusion, the Jones polynomial, and the Casson–Walker invariant, Rev. Mat. Complut. 18 (2005) 387 MR2166517
36 Y Mizuma, An estimate of the ribbon number by the Jones polynomial, Osaka J. Math. 43 (2006) 365 MR2262340
37 D Mullins, The generalized Casson invariant for $2$–fold branched covers of $S^3$ and the Jones polynomial, Topology 32 (1993) 419 MR1217078
38 H Murakami, T Ohtsuki, Finite type invariants of knots via their Seifert matrices, Asian J. Math. 5 (2001) 379 MR1868640
39 H Murakami, T Ohtsuki, S Yamada, Homfly polynomial via an invariant of colored plane graphs, Enseign. Math. $(2)$ 44 (1998) 325 MR1659228
40 K Murasugi, On a certain numerical invariant of link types, Trans. Amer. Math. Soc. 117 (1965) 387 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 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
45 A G Tristram, Some cobordism invariants for links, Proc. Cambridge Philos. Soc. 66 (1969) 251 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 MR1089670
47 O Viro, editor, Topology of manifolds and varieties, Advances in Soviet Mathematics 18, Amer. Math. Soc. (1994)