Tame arcs on wild cells

Seebeck, Charles L.

doi:10.1090/S0002-9939-1971-0281177-X

Tame arcs on wild cells
HTML articles powered by AMS MathViewer

by Charles L. Seebeck

Proc. Amer. Math. Soc. 29 (1971), 197-201

DOI: https://doi.org/10.1090/S0002-9939-1971-0281177-X

PDF | Request permission

Abstract:

We prove here that, for $n \geqq 5$, every cell in ${E^n}$ contains a tame arc and that, for product cells ${B^{m - k}} \times {I^k} \subset {E^{n - k}} \times {E^k} = {E^n}$ , every k-dimensional polyhedron $P \subset {B^{m - k}} \times {I^k}$ is tame in ${E^n}$.

References

R. H. Bing, Each disk in $E^{3}$ contains a tame arc, Amer. J. Math. 84 (1962), 583–590. MR 146811, DOI 10.2307/2372864
R. H. Bing, A wild surface each of whose arcs is tame, Duke Math. J. 28 (1961), 1–15. MR 123302
R. H. Bing and J. M. Kister, Taming complexes in hyperplanes, Duke Math. J. 31 (1964), 491–511. MR 164329
J. L. Bryant and C. L. Seebeck III, Locally nice embeddings of polyhedra, Quart. J. Math. Oxford Ser. (2) 19 (1968), 257–274. MR 234434, DOI 10.1093/qmath/19.1.257
J. L. Bryant and C. L. Seebeck III, Locally nice embeddings in codimension three, Quart. J. Math. Oxford Ser. (2) 21 (1970), 265–272. MR 290376, DOI 10.1093/qmath/21.3.265
A. V. Černavskiĭ, Topological embeddings of manifolds, Dokl. Akad. Nauk SSSR 187 (1969), 1247–1250 (Russian). MR 0259918
Herman Gluck, Embeddings in the trivial range, Ann. of Math. (2) 81 (1965), 195–210. MR 173243, DOI 10.2307/1970614
Tatsuo Homma, On the imbedding of polyhedra in manifolds, Yokohama Math. J. 10 (1962), 5–10. MR 154287
Richard T. Miller, Approximating codimension $3$ embeddings, Ann. of Math. (2) 95 (1972), 406–416. MR 307246, DOI 10.2307/1970867
T. B. Rushing, Everywhere wild cells and spheres, Rocky Mountain J. Math. 2 (1972), no. 2, 249–258. MR 301741, DOI 10.1216/RMJ-1972-2-2-249