An equivalence for the embeddings of cells in a 3-manifold

Daverman, R. J.; Eaton, W. T.

doi:10.1090/S0002-9947-1969-0250280-8

An equivalence for the embeddings of cells in a $3$-manifold
HTML articles powered by AMS MathViewer

by R. J. Daverman and W. T. Eaton

Trans. Amer. Math. Soc. 145 (1969), 369-381

DOI: https://doi.org/10.1090/S0002-9947-1969-0250280-8

PDF | Request permission

References

W. R. Alford, Some “nice” 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. 29–33. MR 0141091
J. J. Andrews and M. L. Curtis, $n$-space modulo an arc, Ann. of Math. (2) 75 (1962), 1–7. MR 139153, DOI 10.2307/1970414
Steve Armentrout, Concerning a wild 3-cell described by Bing, Duke Math. J. 33 (1966), 689–704. MR 198446
Steve Armentrout, Lloyd L. Lininger, and Donald V. Meyer, Equivalent decomposition of $R^{3}$, Pacific J. Math. 24 (1968), 205–227. MR 224070, DOI 10.2140/pjm.1968.24.205
R. H. Bing, A simple closed curve that pierces no disk, J. Math. Pures Appl. (9) 35 (1956), 337–343. MR 81461
R. H. Bing, A surface is tame if its complement is $1$-ULC, Trans. Amer. Math. Soc. 101 (1961), 294–305. MR 131265, DOI 10.1090/S0002-9947-1961-0131265-1
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 and A. Kirkor, An arc is tame in $3$-space if and only if it is strongly cellular, Fund. Math. 55 (1964), 175–180. MR 170330, DOI 10.4064/fm-55-2-175-180
John L. Bryant, Euclidean space modulo a cell, Fund. Math. 63 (1968), 43–51. MR 230298, DOI 10.4064/fm-63-1-43-51
Robert Craggs, Improving the intersection of polyhedra in $3$-manifolds, Illinois J. Math. 12 (1968), 567–586. MR 232367
Robert J. Daverman and William T. Eaton, A dense set of sewings of two crumpled cubes yields $S^{3}$, Fund. Math. 65 (1969), 51–60. MR 243500, DOI 10.4064/fm-65-1-51-60
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

The sum of a real cube and a crumpled cube is

10

11

Kyung Whan Kwun, Product of euclidean spaces modulo an arc, Ann. of Math. (2) 79 (1964), 104–108. MR 159312, DOI 10.2307/1970485
Lloyd L. Lininger, Some results on crumpled cubes, Trans. Amer. Math. Soc. 118 (1965), 534–549. MR 178460, DOI 10.1090/S0002-9947-1965-0178460-7
D. R. McMillan Jr., A criterion for cellularity in a manifold. II, Trans. Amer. Math. Soc. 126 (1967), 217–224. MR 208583, DOI 10.1090/S0002-9947-1967-0208583-7
Donald V. Meyer, $E^{3}$ modulo a $3$-cell, Pacific J. Math. 13 (1963), 193–196. MR 150746, DOI 10.2140/pjm.1963.13.193
Horst Schubert, Knoten und Vollringe, Acta Math. 90 (1953), 131–286 (German). MR 72482, DOI 10.1007/BF02392437