Properly homotopic nontrivial planes are isotopic

Bobby Winters

Fundamenta Mathematicae (1995)

  • Volume: 146, Issue: 2, page 141-152
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Winters, Bobby. "Properly homotopic nontrivial planes are isotopic." Fundamenta Mathematicae 146.2 (1995): 141-152. <http://eudml.org/doc/212057>.

@article{Winters1995,
abstract = {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.},
author = {Winters, Bobby},
journal = {Fundamenta Mathematicae},
keywords = {planes; properly homotopic in a noncompact, orientable, irreducible 3- manifold; end-reduction},
language = {eng},
number = {2},
pages = {141-152},
title = {Properly homotopic nontrivial planes are isotopic},
url = {http://eudml.org/doc/212057},
volume = {146},
year = {1995},
}

TY - JOUR
AU - Winters, Bobby
TI - Properly homotopic nontrivial planes are isotopic
JO - Fundamenta Mathematicae
PY - 1995
VL - 146
IS - 2
SP - 141
EP - 152
AB - 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.
LA - eng
KW - planes; properly homotopic in a noncompact, orientable, irreducible 3- manifold; end-reduction
UR - http://eudml.org/doc/212057
ER -

References

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  1. [BT] M. G. Brin and T. L. Thickstun, 3-manifolds which are end 1-movable, Mem. Amer. Math. Soc. 411 (1989). 
  2. [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. Zbl0323.57008
  3. [BF] E. M. Brown and C. D. Feustel, On properly embedding planes in arbitrary 3-manifolds, Proc. Amer. Math. Soc. 94 (1985), 173-178. Zbl0577.57006
  4. [He] J. Hempel, 3-manifolds, Ann. of Math. Stud. 86, Princeton Univ. Press, 1976. 
  5. [Wa] F. Waldhausen, On irreducible 3-manifolds which are sufficiently large, Ann. of Math. 87 (1968), 56-88. Zbl0157.30603
  6. [W] B. N. Winters, Properly homotopic, nontrivial planes are parallel, Topology Appl. 48 (1992), 235-243. Zbl0814.57009

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