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Transactions of the American Mathematical Society

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A spectral sequence for group presentations with applications to links


Author: Selma Wanna
Journal: Trans. Amer. Math. Soc. 261 (1980), 271-285
MSC: Primary 57M05; Secondary 55T99, 57M25
DOI: https://doi.org/10.1090/S0002-9947-1980-0576875-4
MathSciNet review: 576875
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Abstract | References | Similar Articles | Additional Information

Abstract: A spectral sequence is associated with any presentation of a group G. It turns out that this spectral sequence is independent of the chosen presentation. In particular if G is the fundamental group of a link L in $ {R^3}$ the spectral sequence leads to invariants that compare to the Milnor invariants of L.


References [Enhancements On Off] (What's this?)

  • [1] R. Baer, The higher commutator subgroups of a group, Bull. Amer. Math. Soc. 50 (1944), 143-160. MR 0009954 (5:227g)
  • [2] K. T. Chen, Isotopy invariants of links, Ann. of Math. (2) 56 (1952), 343-353. MR 0049557 (14:193g)
  • [3] R. H. Fox, Free differential calculus. I, Ann. of Math. (2) 57 (1953), 547-560. MR 0053938 (14:843d)
  • [4] A. Frohlich, Baer invariants of algebras, Trans. Amer. Math. Soc. 109 (1963), 221-244. MR 0158920 (28:2142)
  • [5] M. Gutiérrez, The $ \bar \mu $-invariants for groups, Proc. Amer. Math. Soc. 55 (1976), 293-298. MR 0422328 (54:10319)
  • [6] P. Hilton and U. Stammbach, A course in homological algebra, Springer-Verlag, New York, 1971. MR 0346025 (49:10751)
  • [7] J. Milnor, Isotopy of links, Lefschetz Symposium, Princeton Univ. Press, Princeton, N. J., 1957. MR 0092150 (19:1070c)
  • [8] N. Smythe, Isotopy invariants for links and the Alexander matrix, Amer. J. Math. 89 (1967), 693-703. MR 0219056 (36:2139)
  • [9] J. Stallings, Quotients of the powers of the augmentation ideal in a group ring, Ann. of Math. Studies No. 84, Princeton Univ. Press, Princeton, N. J., 1975, pp. 101-118. MR 0379685 (52:590)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1980-0576875-4
Keywords: Group presentation, Baer invariants, spectral sequence, links
Article copyright: © Copyright 1980 American Mathematical Society

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