A remarkable simple closed curve: revisited

Harrold, O. G.

doi:10.1090/S0002-9939-1981-0589155-4

A remarkable simple closed curve: revisited
HTML articles powered by AMS MathViewer

by O. G. Harrold PDF

Proc. Amer. Math. Soc. 81 (1981), 133-136 Request permission

Abstract:

It is shown that the pathology of R. H. Fox’s remarkable simple closed curve is in a sense explained below more complicated than that of some examples of the well-known Fox-Artin paper.

References

R. H. Bing, Locally tame sets are tame, Ann. of Math. (2) 59 (1954), 145–158. MR 61377, DOI 10.2307/1969836
P. H. Doyle and J. G. Hocking, Some results on tame disks and spheres in $E^{3}$, Proc. Amer. Math. Soc. 11 (1960), 832–836. MR 126839, DOI 10.1090/S0002-9939-1960-0126839-2
Ralph H. Fox and Emil Artin, Some wild cells and spheres in three-dimensional space, Ann. of Math. (2) 49 (1948), 979–990. MR 27512, DOI 10.2307/1969408
R. H. Fox and O. G. Harrold, The Wilder arcs, Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 184–187. MR 0140096
Ralph H. Fox, A remarkable simple closed curve, Ann. of Math. (2) 50 (1949), 264–265. MR 30745, DOI 10.2307/1969450
W. Graeub, Die semilinearen Abbildungen, S.-B. Heidelberger Akad. Wiss. Math.-Nat. Kl. 1950 (1950), 205–272 (German). MR 0042709
O. G. Harrold Jr., Locally tame curves and surfaces in three-dimensional manifolds, Bull. Amer. Math. Soc. 63 (1957), 293–305. MR 88718, DOI 10.1090/S0002-9904-1957-10125-6

An Additive Index Theorem for certain wildly embedded curves and surfaces

Edwin E. Moise, Affine structures in $3$-manifolds. VIII. Invariance of the knot-types; local tame imbedding, Ann. of Math. (2) 59 (1954), 159–170. MR 61822, DOI 10.2307/1969837