Properly homotopic nontrivial planes are isotopic

• Autorzy: Bobby Neal Winters
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 57N20: Topology of infinite-dimensional manifolds
• 57M99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1994-1995
• Tom: 146
• Numer: 2
• Strony: 141-152

Daty

wydano

1995

otrzymano

1993-05-25

poprawiono

1994-06-27

Twórcy

autor

Bobby Neal Winters

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

Bibliografia

• [BT] M. G. Brin and T. L. Thickstun, 3-manifolds which are end 1-movable, Mem. Amer. Math. Soc. 411 (1989).
• [BBF] E. M. Brown, M. S. Brown and C. D. Feustel, On properly embedding planes in 3-manifolds, Trans. Amer. Math. Soc. 55 (1976), 461-464.
• [BF] E. M. Brown and C. D. Feustel, On properly embedding planes in arbitrary 3-manifolds, Proc. Amer. Math. Soc. 94 (1985), 173-178.
• [He] J. Hempel, 3-manifolds, Ann. of Math. Stud. 86, Princeton Univ. Press, 1976.
• [Wa] F. Waldhausen, On irreducible 3-manifolds which are sufficiently large, Ann. of Math. 87 (1968), 56-88.
• [W] B. N. Winters, Properly homotopic, nontrivial planes are parallel, Topology Appl. 48 (1992), 235-243.