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$ H\sb{2}$ of the commutator subgroup of a knot group


Author: D. W. Sumners
Journal: Proc. Amer. Math. Soc. 28 (1971), 319-320
MSC: Primary 55.20
DOI: https://doi.org/10.1090/S0002-9939-1971-0275416-9
MathSciNet review: 0275416
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Abstract: A short topological proof is given for the well-known theorem that if $ G$ is a knot group and $ G'$ its commutator subgroup, then $ {H_2}(G';Z) = 0$.


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

  • [1] R. H. Crowell, $ {H_2}$ of subgroups of knot groups, Illinois J. Math. (to appear) MR 0266191 (42:1099)
  • [2] -, $ {H_2}(G')$ for tamely embedded graphs, Quart. J. Math. Oxford Ser. (2) 21 (1970), 25-27. MR 0258013 (41:2660)
  • [3] J. Levine, Polynomial invariants of knots of codimension two, Ann. of Math. (2) 84 (1966), 537-544. MR 34 #808. MR 0200922 (34:808)
  • [4] J. W. Milnor, Infinite cyclic coverings, Conference on the Topology of Manifolds (Michigan State Univ., E. Lansing, Mich., 1967), Prindle, Weber & Schmidt, Boston, Mass., 1968, pp. 115-133. MR 39 #3497. MR 0242163 (39:3497)
  • [5] C. D. Papakryiakopoulos, On Dehn's lemma and the asphericity of knots, Ann. of Math. (2) 66 (1957), 1-26. MR 19, 761. MR 0090053 (19:761a)
  • [6] R. G. Swan, Minimal resolutions for finite groups, Topology 4 (1965), 193-208. MR 31 #3482. MR 0179234 (31:3482)
  • [7] J. H. C. Whitehead, On the asphericity of regions in a $ 3$-sphere, Fund. Math. 32 (1939), 149-166.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0275416-9
Keywords: Commutator subgroup of a knot group, homology of groups, infinite cyclic covering space
Article copyright: © Copyright 1971 American Mathematical Society

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