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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

A short proof of Bing's characterization of $ S^3$

Author(s): Yo'av Rieck
Journal: Proc. Amer. Math. Soc. 135 (2007), 1947-1948.
MSC (2000): Primary 57M40; Secondary 57N12
Posted: January 31, 2007
MathSciNet review: 2286108
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Abstract | References | Similar articles | Additional information

Abstract: We give a short proof of Bing's characterization of $ S^3$: a compact, connected 3-manifold $ M$ is $ S^3$ if and only if every knot in $ M$ is isotopic into a ball.

References:

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R. H. Bing, Necessary and sufficient conditions that a $ 3$-manifold be $ S\sp{3}$, Ann. of Math. (2) 68 (1958), 17-37. MR 0095471 (20:1973)

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Wolfgang Haken, Some results on surfaces in $ 3$-manifolds, Studies in Modern Topology, Math. Assoc. Amer. (distributed by Prentice-Hall, Englewood Cliffs, N.J.), 1968, pp. 39-98. MR 0224071 (36:7118)

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John Hempel, $ 3$-Manifolds, Princeton University Press, Princeton, N. J., 1976, Ann. of Math. Studies, No. 86. MR 0415619 (54:3702)

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William Jaco, Lectures on three-manifold topology, CBMS Regional Conference Series in Mathematics, vol. 43, American Mathematical Society, Providence, R.I., 1980. MR 0565450 (81k:57009)

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William Jaco and J. Hyam Rubinstein, 0-efficient triangulations of 3-manifolds, J. Differential Geom. 65 (2003), no. 1, 61-168. MR 2057531 (2005d:57034)

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H. Kneser, Geschlossene flächen in dreidimensionalen Mannigfaltigkeiten, Jahresbericht der Deut. Math. Verein. 38 (1929), 248-260.

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Martin Scharlemann, Heegaard splittings of 3-manifolds, Low dimensional topology, New Stud. Adv. Math., vol. 3, Int. Press, Somerville, MA, 2003, pp. 25-39. MR 2052244

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Friedhelm Waldhausen, Heegaard-Zerlegungen der $ 3$-Sphäre, Topology 7 (1968), 195-203. MR 0227992 (37:3576)

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Additional Information:

Yo'av Rieck
Affiliation: Department of Mathematical Sciences, 301 SCEN, University of Arkansas, Fayetteville, Arkansas 72701
Email: yoav@uark.edu

DOI: 10.1090/S0002-9939-07-08657-1
PII: S 0002-9939(07)08657-1
Received by editor(s): April 25, 2005
Received by editor(s) in revised form: January 27, 2006
Posted: January 31, 2007
Communicated by: Ronald A. Fintushel
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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