It is proved that two planes that are properly homotopic in a noncompact, orientable, irreducible 3-manifold that is not homeomorphic to are isotopic. The end-reduction techniques of E. M. Brown and C. D. Feustal and M. G. Brin and T. L. Thickstun are used.
@article{bwmeta1.element.bwnjournal-article-fmv146i2p141bwm,
author = {Bobby Winters},
title = {Properly homotopic nontrivial planes are isotopic},
journal = {Fundamenta Mathematicae},
volume = {146},
year = {1995},
pages = {141-152},
zbl = {0835.57008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv146i2p141bwm}
}
Winters, Bobby. Properly homotopic nontrivial planes are isotopic. Fundamenta Mathematicae, Tome 146 (1995) pp. 141-152. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv146i2p141bwm/
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