Properly homotopic nontrivial planes are isotopic

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Department of Mathematics, Pittsburg State University, Pittsburg, Kansas 66762, U.S.A.

It is proved that two planes that are properly homotopic in a noncompact, orientable, irreducible 3-manifold that is not homeomorphic to

ℝ^{3}

are isotopic. The end-reduction techniques of E. M. Brown and C. D. Feustal and M. G. Brin and T. L. Thickstun are used.

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