The classification of links up to link-homotopy

Habegger, Nathan; Lin, Xiao-Song

doi:10.1090/S0894-0347-1990-1026062-0

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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
MathSciNet review: 1026062
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[A] E. Artin, Theory of braids, Ann. of Math. (2) 48 (1947), 101–126. MR 0019087 (8,367a)
[Ba] Gilbert Baumslag, Lecture notes on nilpotent groups, Regional Conference Series in Mathematics, No. 2, American Mathematical Society, Providence, R.I., 1971. MR 0283082 (44 #315)
[B] Joan S. Birman, Braids, links, and mapping class groups, Princeton University Press, Princeton, N.J., 1974. Annals of Mathematics Studies, No. 82. 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 -braids, (3) Closed braid representatives of split links and composite links, (4) Closed braid representatives of the unlink, preprints, Columbia Univ., 1988.
[C] Tim D. Cochran, Derivatives of links: Milnor’s concordance invariants and Massey’s products, Mem. Amer. Math. Soc. 84 (1990), no. 427, x+73. 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] Deborah Louise Goldsmith, Homotopy of braids—in answer to a question of E. Artin, Topology Conference (Virginia Polytech. Inst. and State Univ., Blacksburg, Va., 1973), Springer, Berlin, 1974, pp. 91–96. Lecture Notes in Math., Vol. 375. MR 0356021 (50 #8494)
[G2] Deborah L. Goldsmith, Concordance implies homotopy for classical links in 𝑀³, Comment. Math. Helv. 54 (1979), no. 3, 347–355. MR 543335 (80h:57006), http://dx.doi.org/10.1007/BF02566279
[Gi] Charles H. Giffen, Link concordance implies link homotopy, Math. Scand. 45 (1979), no. 2, 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] Vaughan F. R. Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. (N.S.) 12 (1985), no. 1, 103–111. MR 766964 (86e:57006), http://dx.doi.org/10.1090/S0273-0979-1985-15304-2
[Le1] J. P. Levine, Surgery on links and the \𝑜𝑣𝑒𝑟𝑙𝑖𝑛𝑒𝜇-invariants, Topology 26 (1987), no. 1, 45–61. MR 880507 (88d:57005), http://dx.doi.org/10.1016/0040-9383(87)90020-6
[Le2] J. P. Levine, An approach to homotopy classification of links, Trans. Amer. Math. Soc. 306 (1988), no. 1, 361–387. MR 927695 (88m:57008), http://dx.doi.org/10.1090/S0002-9947-1988-0927695-7
[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. S. Massey, Higher order linking numbers, Conf. on Algebraic Topology (Univ. of Illinois at Chicago Circle, Chicago, Ill., 1968), Univ. of Illinois at Chicago Circle, Chicago, Ill., 1969, pp. 174–205. MR 0254832 (40 #8039)
[M1] John Milnor, Link groups, Ann. of Math. (2) 59 (1954), 177–195. MR 0071020 (17,70e)
[M2] John Milnor, Isotopy of links. Algebraic geometry and topology, A symposium in honor of S. Lefschetz, Princeton University Press, Princeton, N. J., 1957, pp. 280–306. 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] Kent E. Orr, Homotopy invariants of links, Invent. Math. 95 (1989), no. 2, 379–394. MR 974908 (90a:57012), http://dx.doi.org/10.1007/BF01393902
[P] Richard Porter, Milnor’s 𝜇-invariants and Massey products, Trans. Amer. Math. Soc. 257 (1980), no. 1, 39–71. MR 549154 (81a:57021), http://dx.doi.org/10.1090/S0002-9947-1980-0549154-9
[S] John Stallings, Homology and central series of groups, J. Algebra 2 (1965), 170–181. MR 0175956 (31 #232)
[T] V. G. Turaev, The Milnor invariants and Massey products, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 66 (1976), 189–203, 209–210 (Russian, with English summary). Studies in topology, II. 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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