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

Author:

Daverman Robert J.

Abstract

For n 7 n \geqslant 7 we describe an ( n 1 ) (n - 1) -sphere Σ \Sigma wildly embedded in the n n -sphere yet every point of Σ \Sigma has arbitrarily small neighborhoods bounded by flat ( n 1 ) (n - 1) -spheres, each intersecting Σ \Sigma in an ( n 2 ) (n - 2) -sphere. Not only do these examples for large n n run counter to what can occur when n = 3 n = 3 , 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 n = 3 n = 3 and also partially illustrate the sharpness of another high-dimensional taming theorem due to Bryant and Lacher.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference20 articles.

1. The Vietoris mapping theorem for bicompact spaces;Begle, Edward G.;Ann. of Math. (2),1950

2. Embeddings with mapping cylinder neighborhoods;Bryant, J. L.;Topology,1975

3. Characterizations of tame surfaces in 𝐸³;Burgess, C. E.;Trans. Amer. Math. Soc.,1965

4. Characterization of taming sets on 2-spheres;Cannon, J. W.;Trans. Amer. Math. Soc.,1970

5. 𝑈𝐿𝐶 properties in neighbourhoods of embedded surfaces and curves in 𝐸³;Cannon, J. W.;Canadian J. Math.,1973

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