Geometry & Topology Volume 16, issue 2 (2012)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Milnor invariants and the HOMFLYPT Polynomial

Jean-Baptiste Meilhan and Akira Yasuhara

Geometry & Topology 16 (2012) 889–917

DOI: 10.2140/gt.2012.16.889

Bibliography

1	D Bar-Natan, Vassiliev homotopy string link invariants, J. Knot Theory Ramifications 4 (1995) 13 MR1321289
2	J C Cha, The effect of mutation on link concordance, 3-manifolds, and the Milnor invariants, J. Knot Theory Ramifications 15 (2006) 239 MR2207908
3	T D Cochran, Concordance invariance of coefficients of Conway's link polynomial, Invent. Math. 82 (1985) 527 MR811549
4	C H Giffen, Link concordance implies link homotopy, Math. Scand. 45 (1979) 243 MR580602
5	D L Goldsmith, Concordance implies homotopy for classical links in $M^{3}$, Comment. Math. Helv. 54 (1979) 347 MR543335
6	M Gusarov, On $n$–equivalence of knots and invariants of finite degree, from: "Topology of manifolds and varieties" (editor O Viro), Adv. Soviet Math. 18, Amer. Math. Soc. (1994) 173 MR1296895
7	N Habegger, X S Lin, The classification of links up to link-homotopy, J. Amer. Math. Soc. 3 (1990) 389 MR1026062
8	N Habegger, G Masbaum, The Kontsevich integral and Milnor's invariants, Topology 39 (2000) 1253 MR1783857
9	K Habiro, Claspers and finite type invariants of links, Geom. Topol. 4 (2000) 1 MR1735632
10	S Horiuchi, The Jacobi diagram for a $C_n$–move and the HOMFLY polynomial, J. Knot Theory Ramifications 16 (2007) 227 MR2306216
11	T Kanenobu, $\mathbf C_n$–moves and the HOMFLY polynomials of links, Bol. Soc. Mat. Mexicana 10 (2004) 263 MR2199353
12	T Kanenobu, Y Miyazawa, HOMFLY polynomials as Vassiliev link invariants, from: "Knot theory (Warsaw, 1995)" (editors V F R Jones, J Kania-Bartoszynska, J H Przytycki, P Traczyk, V Turaev), Banach Center Publ. 42, Polish Acad. Sci. (1998) 165 MR1634455
13	J Levine, A factorization of the Conway polynomial, Comment. Math. Helv. 74 (1999) 27 MR1677110
14	W B R Lickorish, K C Millett, A polynomial invariant of oriented links, Topology 26 (1987) 107 MR880512
15	X S Lin, Power series expansions and invariants of links, from: "Geometric topology (Athens, GA, 1993)" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 184 MR1470727
16	G Masbaum, A Vaintrob, Milnor numbers, spanning trees, and the Alexander–Conway polynomial, Adv. Math. 180 (2003) 765 MR2020557
17	J B Meilhan, On Vassiliev invariants of order two for string links, J. Knot Theory Ramifications 14 (2005) 665 MR2162120
18	J B Meilhan, A Yasuhara, On $C_n$–moves for links, Pacific J. Math. 238 (2008) 119 MR2443510
19	J Milnor, Link groups, Ann. of Math. 59 (1954) 177 MR0071020
20	J Milnor, Isotopy of links. Algebraic geometry and topology, from: "A symposium in honor of S Lefschetz" (editors R H Fox, D C Spencer, A W Tucker), Princeton Univ. Press (1957) 280 MR0092150
21	K Murasugi, On Milnor's invariant for links, Trans. Amer. Math. Soc. 124 (1966) 94 MR0198453
22	M Polyak, On Milnor's triple linking number, C. R. Acad. Sci. Paris Sér. I Math. 325 (1997) 77 MR1461401
23	T Stanford, Braid commutators and Vassiliev invariants, Pacific J. Math. 174 (1996) 269 MR1398378
24	L Traldi, Milnor's invariants and the completions of link modules, Trans. Amer. Math. Soc. 284 (1984) 401 MR742432
25	L Traldi, Conway's potential function and its Taylor series, Kobe J. Math. 5 (1988) 233 MR990824
26	A Yasuhara, Classification of string links up to self delta-moves and concordance, Algebr. Geom. Topol. 9 (2009) 265 MR2482076
27	A Yasuhara, Self delta-equivalence for links whose Milnor's isotopy invariants vanish, Trans. Amer. Math. Soc. 361 (2009) 4721 MR2506425