On properly embedding planes in 3-manifolds
E. M. Brown, Marianne S. Brown, Charles D. Feustel · Proceedings of the American Mathematical Society · 1976
In this paper we prove an analog of the loop theorem for a certain class of noncompact 3 3 -manifolds. In particular, we show that the existence of a “nontrivial” proper map of a plane into a 3 3 -manifold implies the existence of a nontrivial proper embedding of a plane into a 3 3 -manifold.