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A counterexample to conjectures of Papakyriakopoulos and Swarup


Author: James McCool
Journal: Proc. Amer. Math. Soc. 81 (1981), 193-194
MSC: Primary 20F05; Secondary 20E06, 57M40
DOI: https://doi.org/10.1090/S0002-9939-1981-0593455-1
MathSciNet review: 593455
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Abstract: In [5] Swarup states a group theoretic conjecture $ {\text{P2}}$ and shows that $ {\text{P1}} \Rightarrow {\text{P2}} \Rightarrow $ the Poincaré conjecture, where $ {\text{P1}}$ is a conjecture of Papakyriakopoulos [3]. We give a counterexample to conjecture $ {\text{P2}}$.


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

  • [1] R. C. Lyndon and P. Schupp, Combinatorial group theory, Springer-Verlag, Berlin and New York, 1977. MR 0577064 (58:28182)
  • [2] W. Magnus, A. Karrass and D. Solitar, Combinatorial group theory, Wiley, New York, 1966.
  • [3] C. D. Papakyriakopoulos, A reduction of Poincaré conjecture to group theoretic conjectures, Ann. of Math. (2) 77 (1963), 250-305. MR 0145496 (26:3027)
  • [4] A. Shenitzer, Decomposition of a group with a single defining relation into a free product, Proc. Amer. Math. Soc. 6 (1955), 273-279. MR 0069174 (16:995c)
  • [5] G. A. Swarup, Two reductions of the Poincaré conjecture, Bull. Amer. Math. Soc. N.S. 1 (1979), 774-777. MR 537630 (82j:57005)

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DOI: https://doi.org/10.1090/S0002-9939-1981-0593455-1
Article copyright: © Copyright 1981 American Mathematical Society

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