𝔐³ admitting a certain embedding of 𝔓² is a pseudo 𝔓³

Feustel, C. D.

doi:10.1090/S0002-9939-1970-0263083-9

$\mathfrak {M}^3$ 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.

John Stallings, On the loop theorem, Ann. of Math. (2) 72 (1960), 12–19. MR 121796, DOI https://doi.org/10.2307/1970146