# Properly homotopic nontrivial planes are isotopic

Fundamenta Mathematicae (1995)

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

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topWinters, 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

top- [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. Zbl0323.57008
- [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
- [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. Zbl0157.30603
- [W] B. N. Winters, Properly homotopic, nontrivial planes are parallel, Topology Appl. 48 (1992), 235-243. Zbl0814.57009

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