The classification of links up to link-homotopy
HTML articles powered by AMS MathViewer
- by Nathan Habegger and Xiao-Song Lin
- J. Amer. Math. Soc. 3 (1990), 389-419
- DOI: https://doi.org/10.1090/S0894-0347-1990-1026062-0
- PDF | Request permission
References
- E. Artin, Theory of braids, Ann. of Math. (2) 48 (1947), 101–126. MR 19087, DOI 10.2307/1969218
- Gilbert Baumslag, Lecture notes on nilpotent groups, Regional Conference Series in Mathematics, No. 2, American Mathematical Society, Providence, R.I., 1971. MR 0283082
- Joan S. Birman, Braids, links, and mapping class groups, Annals of Mathematics Studies, No. 82, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1974. MR 0375281 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.
- 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, DOI 10.1090/memo/0427 J.-Y. le Dimet, Cobordisme d’enlacements de disques, Mém. Soc. Math. France, no. 32, Supplément Bull. Soc. Math. France 116 (1988). R. Fenn (ed.), Low dimensional topology, London Math. Soc. Lecture Note Ser., vol. 95, Cambridge Univ. Press, London, 1985.
- 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) Lecture Notes in Math., Vol. 375, Springer, Berlin, 1974, pp. 91–96. MR 0356021
- Deborah L. Goldsmith, Concordance implies homotopy for classical links in $M^{3}$, Comment. Math. Helv. 54 (1979), no. 3, 347–355. MR 543335, DOI 10.1007/BF02566279
- Charles H. Giffen, Link concordance implies link homotopy, Math. Scand. 45 (1979), no. 2, 243–254. MR 580602, DOI 10.7146/math.scand.a-11839 N. Habegger and X.-S. Lin, On Milnor’s $\overline \mu$-invariants and concordance classification of links, (in preparation).
- 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, DOI 10.1090/S0273-0979-1985-15304-2
- J. P. Levine, Surgery on links and the $\overline \mu$-invariants, Topology 26 (1987), no. 1, 45–61. MR 880507, DOI 10.1016/0040-9383(87)90020-6
- J. P. Levine, An approach to homotopy classification of links, Trans. Amer. Math. Soc. 306 (1988), no. 1, 361–387. MR 927695, DOI 10.1090/S0002-9947-1988-0927695-7 X.-S. Lin, Artin-type representation theorems and Milnor’s $\overline \mu$-invariants, Ph.D. thesis, Univ. of California, San Diego, 1988.
- 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
- John Milnor, Link groups, Ann. of Math. (2) 59 (1954), 177–195. MR 71020, DOI 10.2307/1969685
- 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 W. Magnus, A. Karrass, and D. Solitar, Combinatorial group theory, Pure and Appl. Math., vol. XIII, Interscience, NY, 1966.
- Kent E. Orr, Homotopy invariants of links, Invent. Math. 95 (1989), no. 2, 379–394. MR 974908, DOI 10.1007/BF01393902
- Richard Porter, Milnor’s $\bar \mu$-invariants and Massey products, Trans. Amer. Math. Soc. 257 (1980), no. 1, 39–71. MR 549154, DOI 10.1090/S0002-9947-1980-0549154-9
- John Stallings, Homology and central series of groups, J. Algebra 2 (1965), 170–181. MR 175956, DOI 10.1016/0021-8693(65)90017-7
- 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 E. Witten, Quantum field theory and the Jones polynomial, preprint, Institute for Advanced Study, Princeton, NJ, 1988.
Bibliographic Information
- © Copyright 1990 American Mathematical Society
- 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