A counterexample to conjectures of Papakyriakopoulos and Swarup
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- by James McCool PDF
- Proc. Amer. Math. Soc. 81 (1981), 193-194 Request permission
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
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- C. D. Papakyriakopoulos, A reduction of the Poincaré conjecture to group theoretic conjectures, Ann. of Math. (2) 77 (1963), 250–305. MR 145496, DOI 10.2307/1970216
- Abe Shenitzer, Decomposition of a group with a single defining relation into a free product, Proc. Amer. Math. Soc. 6 (1955), 273–279. MR 69174, DOI 10.1090/S0002-9939-1955-0069174-1
- G. A. Swarup, Two reductions of the Poincaré conjecture, Bull. Amer. Math. Soc. (N.S.) 1 (1979), no. 5, 774–777. MR 537630, DOI 10.1090/S0273-0979-1979-14662-7
Additional Information
- © Copyright 1981 American Mathematical Society
- 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