Embedding phenomena based upon decomposition theory: locally spherical but wild codimension one spheres

Author:
Robert J. Daverman

Journal:
Proc. Amer. Math. Soc. **90** (1984), 139-144

MSC:
Primary 57N50; Secondary 54B15, 57M30, 57N15, 57N45

DOI:
https://doi.org/10.1090/S0002-9939-1984-0722432-5

MathSciNet review:
722432

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Abstract: For we describe an -sphere wildly embedded in the -sphere yet every point of has arbitrarily small neighborhoods bounded by flat -spheres, each intersecting in an -sphere. Not only do these examples for large run counter to what can occur when , they also illustrate the sharpness of high-dimensional taming theorems developed by Cannon and Harrold and Seebeck. Furthermore, despite their wildness, they have mapping cylinder neighborhoods, which both run counter to what is possible when and also partially illustrate the sharpness of another high-dimensional taming theorem due to Bryant and Lacher.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1984-0722432-5

Keywords:
Wild embedding,
locally flat,
codimension one sphere,
locally spherical,
locally weakly flat,
homology cell,
upper semicontinuous decomposition

Article copyright:
© Copyright 1984
American Mathematical Society