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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(e) ISSN 0894-0347(p)

     

The classification of links up to link-homotopy

Author(s): Nathan Habegger; Xiao-Song Lin
Journal: J. Amer. Math. Soc. 3 (1990), 389-419.
MSC: Primary 57M25
MathSciNet review: 1026062
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References:

[A]
E. Artin, The theory of braids, Ann. of Math. 48 (1947), 101-126. MR 0019087 (8:367a)

[Ba]
G. Baumslag, Lecture notes on nilpotent groups, CBMS Regional Conf. Ser. in Math., vol. 2, Amer. Math. Soc., Providence, RI, 1971. MR 0283082 (44:315)

[B]
J. Birman, Braids, links and mapping class groups, Ann. of Math. Stud., vol. 82, Princeton Univ. Press, Princeton, NJ, 1974. MR 0375281 (51:11477)

[BM]
J. Birman and W. Menasco, (1) Studying links via closed braids, (2) Studying links via closed braids II: Classifying links which are closed $             3$-braids, (3) Closed braid representatives of split links and composite links, (4) Closed braid representatives of the unlink, preprints, Columbia Univ., 1988.

[C]
T. Cochran, Derivatives of links: Milnor's concordance invariants and Massey's products, Mem. Amer. Math. Soc., vol. 84, Amer. Math. Soc., Providence, RI, 1990.. MR 1042041 (91c:57005)

[D]
J.-Y. le Dimet, Cobordisme d'enlacements de disques, Mém. Soc. Math. France, no. 32, Supplément Bull. Soc. Math. France 116 (1988).

[F]
R. Fenn (ed.), Low dimensional topology, London Math. Soc. Lecture Note Ser., vol. 95, Cambridge Univ. Press, London, 1985.

[G1]
D. Goldsmith, Homotopy of links: in answer to a question of E. Artin, Topology Conference, Lecture Notes in Math., vol 357, Springer-Verlag, Berlin, Heidelberg, New York, 1974, pp. 91-96. MR 0356021 (50:8494)

[G2]
-, Concordance implies homotopy for classical links in $ {M^3}$, Comment. Math. Helv. 54 (1979), 347-355. MR 543335 (80h:57006)

[Gi]
C. Giffen, Link concordance implies link homotopy, Math. Scand. 45 (1979), 243-254. MR 580602 (82a:57005)

[HL]
N. Habegger and X.-S. Lin, On Milnor's $ \overline \mu $-invariants and concordance classification of links, (in preparation).

[J]
V. Jones, A polynomial invariant for links via von Neuman algebras, Bull. Amer. Math. Soc. 12 (1985), 103-111. MR 766964 (86e:57006)

[Le1]
J. Levine, Surgery equivalence of links, Topology 26 (1987), 45-61. MR 880507 (88d:57005)

[Le2]
-, An approach to homotopy classification of links, Trans. Amer. Math. Soc. 306 (1988), 361-387. MR 927695 (88m:57008)

[L]
X.-S. Lin, Artin-type representation theorems and Milnor's $             \overline \mu $-invariants, Ph.D. thesis, Univ. of California, San Diego, 1988.

[Ma]
W. Massey, Higher order linking numbers, Proc. Conference on Algebraic Topology, Univ. of Illinois, Chicago Circle, 1968, pp. 174-205. MR 0254832 (40:8039)

[M1]
J. Milnor, Link groups, Ann. of Math. 59 (1954), 177-195. MR 0071020 (17:70e)

[M2]
-, Isotopy of links, Algebraic Geometry and Topology, Princeton Univ. Press, Princeton, NJ, 1957. MR 0092150 (19:1070c)

[MKS]
W. Magnus, A. Karrass, and D. Solitar, Combinatorial group theory, Pure and Appl. Math., vol. XIII, Interscience, NY, 1966.

[O]
K. Orr, Homotopy invariants of links, Invent. Math. 95 (1989), 379-394. MR 974908 (90a:57012)

[P]
R. Porter, Milnor's $ \overline \mu $-invariants and Massey products, Trans. Amer. Math. Soc. 257 (1980), 39-71. MR 549154 (81a:57021)

[S]
J. Stallings, Homology and central series of groups, J. Algebra 20 (1965), 170-181. MR 0175956 (31:232)

[T]
V. G. Turaev, The Milnor invariants and Massey products, J. Soviet Math. 66 (1976), 189-203. MR 0451251 (56:9538)

[W]
E. Witten, Quantum field theory and the Jones polynomial, preprint, Institute for Advanced Study, Princeton, NJ, 1988.

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Additional Information:

DOI: 10.1090/S0894-0347-1990-1026062-0
PII: S0894-0347-1990-1026062-0
Copyright of article: Copyright 1990, American Mathematical Society




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