taming sets for crumpled cubes. III. Horizontal sections in spheres
Author:
James W. Cannon
Journal:
Trans. Amer. Math. Soc. 161 (1971), 447456
MSC:
Primary 54.78
MathSciNet review:
0282355
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Abstract: We prove that a 2sphere S in is tame if each horizontal section of S has at most four components. Since there are wild spheres in whose horizontal sections have at most five components, this result is, in a sense, best possible. Much can nevertheless be said, however, even if certain sections have more than five components; and we show that the wildness of a 2sphere S in is severely restricted by the requirement that each of the horizontal sections of S have at most finitely many components that separate S.
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 R. A. Jensen, Cross sectionally connected 2spheres are tame, Bull. Amer. Math. Soc. 76 (1970), 10361038. MR 0270352 (42:5241)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197102823550
PII:
S 00029947(1971)02823550
Keywords:
Taming sets,
taming sets,
crumpled cubes,
slices in 2spheres,
surfaces in 3manifolds,
2spheres in
Article copyright:
© Copyright 1971
American Mathematical Society
