Wild cells in 𝐸⁴ in which every arc is tame

Daverman, Robert J.

doi:10.1090/S0002-9939-1972-0295312-1

Wild cells in $E\sp{4}$ in which every arc is tame

Author: Robert J. Daverman
Journal: Proc. Amer. Math. Soc. 34 (1972), 270-272
MSC: Primary 57A15
DOI: https://doi.org/10.1090/S0002-9939-1972-0295312-1
MathSciNet review: 0295312
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Abstract: Seebeck has proved that if an m-cell C in Euclidean n-space ${E^n}$ factors k-times, $m \leqq n - 2$ , and $n \geqq 5$ , then every embedding of a compact k-dimensional polyhedron in C is tame relative to ${E^n}$ . We prove the analogous result for and $m \leqq 3$ .

[1] R. H. Bing, Pushing a 2-sphere into its complement, Michigan Math. J. 11 (1964), 33–45. MR 160194
[2] J. L. Bryant, On embeddings with locally nice cross-sections, Trans. Amer. Math. Soc. 155 (1971), 327–332. MR 276983, https://doi.org/10.1090/S0002-9947-1971-0276983-6
[3] J. W. Cannon, Characterizations of tame subsets of 2-spheres in three-dimensional space, Notices Amer. Math. Soc. 17 (1970), 469. Abstract #70T-G43.
[4] R. J. Daverman and W. T. Eaton, An equivalence for the embeddings of cells in a 3-manifold, Trans. Amer. Math. Soc. 145 (1969), 369–381. MR 250280, https://doi.org/10.1090/S0002-9947-1969-0250280-8
[5] Charles L. Seebeck III, Tame arcs on wild cells, Proc. Amer. Math. Soc. 29 (1971), 197–201. MR 281177, https://doi.org/10.1090/S0002-9939-1971-0281177-X
[6] R. B. Sher, Tame polyhedra in wild cells and spheres, Proc. Amer. Math. Soc. 30 (1971), 169–174. MR 281178, https://doi.org/10.1090/S0002-9939-1971-0281178-1