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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

$ \mathfrak{M}^3$ admitting a certain embedding of $ P^2$ is a pseudo $ P^3$


Author: C. D. Feustel
Journal: Proc. Amer. Math. Soc. 26 (1970), 215-216
MSC: Primary 57.01
DOI: https://doi.org/10.1090/S0002-9939-1970-0263083-9
MathSciNet review: 0263083
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Abstract: Let $ M$ be a $ 3$-manifold and $ {P^2}$ projective $ 2$-space. In this paper it is shown that if there exists an embedding $ f:{P^2} \to M$ such that $ f{ \ast _2}:{\pi _2}({P^2}) \to {\pi _2}(M)$ is trivial, then $ M$ is, except for a fake cell, projective $ 3$-space.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0263083-9
Keywords: $ 3$-manifold, projective $ 3$-space, projective plane
Article copyright: © Copyright 1970 American Mathematical Society