Conditions implying that a $2$-sphere is almost tame
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- by L. D. Loveland
- Trans. Amer. Math. Soc. 131 (1968), 170-181
- DOI: https://doi.org/10.1090/S0002-9947-1968-0224074-2
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References
- W. R. Alford, Some βniceβ wild $2$-spheres in $E^{3}$, Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) Prentice-Hall, Englewood Cliffs, N.J., 1962, pp.Β 29β33. MR 0141091
- R. H. Bing, Locally tame sets are tame, Ann. of Math. (2) 59 (1954), 145β158. MR 61377, DOI 10.2307/1969836
- R. H. Bing, An alternative proof that $3$-manifolds can be triangulated, Ann. of Math. (2) 69 (1959), 37β65. MR 100841, DOI 10.2307/1970092
- R. H. Bing, A surface is tame if its complement is $1$-ULC, Trans. Amer. Math. Soc. 101 (1961), 294β305. MR 131265, DOI 10.1090/S0002-9947-1961-0131265-1
- R. H. Bing, Approximating surfaces with polyhedral ones, Ann. of Math. (2) 65 (1957), 465β483. MR 87090
- R. H. Bing, Approximating surfaces from the side, Ann. of Math. (2) 77 (1963), 145β192. MR 150744, DOI 10.2307/1970203
- R. H. Bing, Pushing a 2-sphere into its complement, Michigan Math. J. 11 (1964), 33β45. MR 160194
- R. H. Bing, Each disk in $E^{3}$ contains a tame arc, Amer. J. Math. 84 (1962), 583β590. MR 146811, DOI 10.2307/2372864
- R. H. Bing, Retractions onto spheres, Amer. Math. Monthly 71 (1964), 481β484. MR 162236, DOI 10.2307/2312583
- C. E. Burgess, Characterizations of tame surfaces in $E^{3}$, Trans. Amer. Math. Soc. 114 (1965), 80β97. MR 176456, DOI 10.1090/S0002-9947-1965-0176456-2
- C. E. Burgess, Criteria for a $2$-sphere in $S^{3}$ to be tame modulo two points, Michigan Math. J. 14 (1967), 321β330. MR 216481
- P. H. Doyle and J. G. Hocking, Some results on tame disks and spheres in $E^{3}$, Proc. Amer. Math. Soc. 11 (1960), 832β836. MR 126839, DOI 10.1090/S0002-9939-1960-0126839-2
- David S. Gillman, Note concerning a wild sphere of Bing, Duke Math. J. 31 (1964), 247β254. MR 161317
- John Hempel, A surface in $S^{3}$ is tame if it can be deformed into each complementary domain, Trans. Amer. Math. Soc. 111 (1964), 273β287. MR 160195, DOI 10.1090/S0002-9947-1964-0160195-7 β, Free surfaces in ${S^3}$, (to appear).
- L. D. Loveland, Tame surfaces and tame subsets of spheres in $E^{3}$, Trans. Amer. Math. Soc. 123 (1966), 355β368. MR 199850, DOI 10.1090/S0002-9947-1966-0199850-3
- Edwin E. Moise, Affine structures in $3$-manifolds. VIII. Invariance of the knot-types; local tame imbedding, Ann. of Math. (2) 59 (1954), 159β170. MR 61822, DOI 10.2307/1969837
- C. D. Papakyriakopoulos, On Dehnβs lemma and the asphericity of knots, Ann. of Math. (2) 66 (1957), 1β26. MR 90053, DOI 10.2307/1970113
- C. D. Papakyriakopoulos, On solid tori, Proc. London Math. Soc. (3) 7 (1957), 281β299. MR 87944, DOI 10.1112/plms/s3-7.1.281
Bibliographic Information
- © Copyright 1968 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 131 (1968), 170-181
- MSC: Primary 54.78
- DOI: https://doi.org/10.1090/S0002-9947-1968-0224074-2
- MathSciNet review: 0224074