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The classification of links up to link-homotopy


Authors: Nathan Habegger and Xiao-Song Lin
Journal: J. Amer. Math. Soc. 3 (1990), 389-419
MSC: Primary 57M25
DOI: https://doi.org/10.1090/S0894-0347-1990-1026062-0
MathSciNet review: 1026062
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  • [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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DOI: https://doi.org/10.1090/S0894-0347-1990-1026062-0
Article copyright: © Copyright 1990 American Mathematical Society

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