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A surface in is tame if it can be deformed into each complementary domain
Author:
John Hempel
Journal:
Trans. Amer. Math. Soc. 111 (1964), 273-287
MSC:
Primary 54.75
MathSciNet review:
0160195
Full-text PDF Free Access
References |
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Additional Information
- [1]
J. W. Alexander, On the subdivision of 3-space by polyhedra, Proc. Nat. Acad. Sci. U.S.A. 10 (1924), 10-19.
- [2]
R.
H. Bing, Conditions under which a surface in 𝐸³ is
tame, Fund. Math. 47 (1959), 105–139. MR 0107229
(21 #5954)
- [3]
R.
H. Bing, A surface is tame if its complement is
1-ULC, Trans. Amer. Math. Soc. 101 (1961), 294–305. MR 0131265
(24 #A1117), http://dx.doi.org/10.1090/S0002-9947-1961-0131265-1
- [4]
-, Each disk in each 3-manifold is pierced by a tame arc, Amer. Math. Soc. Notices 6 (1959), 510.
- [5]
Samuel
Eilenberg and Norman
Steenrod, Foundations of algebraic topology, Princeton
University Press, Princeton, New Jersey, 1952. MR 0050886
(14,398b)
- [6]
Ralph
H. Fox and Emil
Artin, Some wild cells and spheres in three-dimensional space,
Ann. of Math. (2) 49 (1948), 979–990. MR 0027512
(10,317g)
- [7]
Witold
Hurewicz and Henry
Wallman, Dimension Theory, Princeton Mathematical Series, v.
4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
(3,312b)
- [8]
Edwin
E. Moise, Affine structures in 3-manifolds. V. The triangulation
theorem and Hauptvermutung, Ann. of Math. (2) 56
(1952), 96–114. MR 0048805
(14,72d)
- [9]
C.
D. Papakyriakopoulos, On Dehn’s lemma and the asphericity of
knots, Ann. of Math. (2) 66 (1957), 1–26. MR 0090053
(19,761a)
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D.
E. Sanderson, Isotopy in 3-manifolds. I. Isotopic
deformations of 2-cells and 3-cells, Proc.
Amer. Math. Soc. 8
(1957), 912–922. MR 0090052
(19,760d), http://dx.doi.org/10.1090/S0002-9939-1957-0090052-8
- [1]
- J. W. Alexander, On the subdivision of 3-space by polyhedra, Proc. Nat. Acad. Sci. U.S.A. 10 (1924), 10-19.
- [2]
- R. H. Bing, Conditions under which a surface in
is tame, Fund. Math. 47 (1959), 105-139. MR 0107229 (21:5954)
- [3]
- -, A surface is tame if its complement is 1-ULC, Trans. Amer. Math. Soc. 101 (1961), 294-305. MR 0131265 (24:A1117)
- [4]
- -, Each disk in each 3-manifold is pierced by a tame arc, Amer. Math. Soc. Notices 6 (1959), 510.
- [5]
- S. Eilenberg and N. Steenrod, Foundations of algebraic topology, Princeton Univ. Press, Princeton, N.J., 1952. MR 0050886 (14:398b)
- [6]
- Ralph H. Fox and Emil Artin, Some wild cells and spheres in three-dimensional space, Ann. of Math. (2) 49 (1948), 979-990. MR 0027512 (10:317g)
- [7]
- W. Hurewicz and H. Wallman, Dimension theory, Princeton Univ. Press, Princeton N. J., 1948. MR 0006493 (3:312b)
- [8]
- E. E. Moise, Affine structures in 3-manifolds. V. The triangulation theorem and Hauptvermutung, Ann. of Math. (2) 56 (1952), 96-114. MR 0048805 (14:72d)
- [9]
- C. D. Papakyriakopoulos, On Dehn's lemma and the asphericity of knots, Ann. of Math. (2) 66 (1957), 1-26. MR 0090053 (19:761a)
- [10]
- D. E. Sanderson, Isotopies in 3-manifolds. I, Proc. Amer. Math. Soc. 8 (1957), 912-922. MR 0090052 (19:760d)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1964-0160195-7
PII:
S 0002-9947(1964)0160195-7
Article copyright:
© Copyright 1964 American Mathematical Society
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