-taming sets for crumpled cubes. III. Horizontal sections in -spheres

Author:
James W. Cannon

Journal:
Trans. Amer. Math. Soc. **161** (1971), 447-456

MSC:
Primary 54.78

MathSciNet review:
0282355

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that a 2-sphere *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 2-sphere *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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DOI:
https://doi.org/10.1090/S0002-9947-1971-0282355-0

Keywords:
Taming sets,
-taming sets,
crumpled cubes,
slices in 2-spheres,
surfaces in 3-manifolds,
2-spheres in

Article copyright:
© Copyright 1971
American Mathematical Society