The fundamental ideal and $\pi _{2}$ of higher dimensional knots
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- by S. J. Lomonaco
- Proc. Amer. Math. Soc. 38 (1973), 431-433
- DOI: https://doi.org/10.1090/S0002-9939-1973-0339193-7
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Abstract:
Let $({S^4},k({S^2}))$ be a knot formed by spinning a polyhedral arc $\alpha$ about the standard $2$-sphere ${S^2}$ in the $3$-sphere ${S^3}$. Then the second homotopy group of ${S^4} - k({S^2})$ as a $Z{\pi _1}$-module is isomorphic to each of the following: (1) The fundamental ideal modulo the left ideal generated by $a - 1$, where $a$ is the image in ${\pi _1}({S^4} - k({S^2}))$ of a generator of ${\pi _1}({S^2} - \alpha )$. (2) The first homology group of the kernel of ${\pi _1}({S^3} - k({S^2})) \to {\pi _1}({S^4} - k({S^2}))$References
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Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 431-433
- MSC: Primary 57C45
- DOI: https://doi.org/10.1090/S0002-9939-1973-0339193-7
- MathSciNet review: 0339193