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Extensions of Dehn's lemma and the loop theorem
Author:
David W. Henderson
Journal:
Trans. Amer. Math. Soc. 120 (1965), 448-469
MSC:
Primary 55.20
MathSciNet review:
0187233
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References |
Similar Articles |
Additional Information
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R.
H. Bing, Locally tame sets are tame, Ann. of Math. (2)
59 (1954), 145–158. MR 0061377
(15,816d)
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-, Approximating surfaces with polyhedral ones, Ann. of Math. 61 (1957), 456-483.
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, Topology of -Manifolds and Related Topics, ed. by M. K. Fort, Jr., Prentice-Hall, Englewood Cliffs, N. J., 1962.
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H. Bing, Approximating surfaces from the side, Ann. of Math.
(2) 77 (1963), 145–192. MR 0150744
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Scott Cairns, Introductory topology, The Ronald Press Co., New
York, 1961. MR
0119198 (22 #9964)
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81 (1959), 889–892. MR 0108552
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H. Edwards Jr., Concentricity in 3-manifolds,
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(31 #2716), http://dx.doi.org/10.1090/S0002-9947-1964-0178459-X
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David
W. Henderson, Self-unlinked simple closed
curves, Trans. Amer. Math. Soc. 120 (1965), 470–480. MR 0187234
(32 #4687), http://dx.doi.org/10.1090/S0002-9947-1965-0187234-2
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David
W. Henderson, Relative general position, Pacific J. Math.
18 (1966), 513–523. MR 0200933
(34 #819)
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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)
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C.
D. Papakyriakopoulos, On solid tori, Proc. London Math. Soc.
(3) 7 (1957), 281–299. MR 0087944
(19,441d)
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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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H. Seifert and W. Threlfall, Lehrbuch der Topologie, Teubner, Leipzig, 1934.
- [14]
Arnold
Shapiro and J.
H. C. Whitehead, A proof and extension of Dehn’s
lemma, Bull. Amer. Math. Soc. 64 (1958), 174–178. MR 0103474
(21 #2242), http://dx.doi.org/10.1090/S0002-9904-1958-10198-6
- [15]
John
Stallings, On the loop theorem, Ann. of Math. (2)
72 (1960), 12–19. MR 0121796
(22 #12526)
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-, The piece-wise linear structures in Euclidean space, Proc. Cambridge Philos. Soc. 58 (1962), 481-188.
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J. H. C. Whitehead, Simplicial spaces, nuclei and
-groups, Proc. London Math. Soc 45 (1939), 243-327.
- [18]
J.
H. C. Whitehead, Note on manifolds, Quart. J. Math., Oxford
Ser. 12 (1941), 26–29. MR 0004781
(3,60h)
- [19]
E.
C. Zeeman, Relative simplicial approximation, Proc. Cambridge
Philos. Soc. 60 (1964), 39–43. MR 0158403
(28 #1626)
- [1]
- R. H. Bing, Locally tame sets are tame, Ann. of Math. 59 (1954), 145-158. MR 0061377 (15:816d)
- [2]
- -, Approximating surfaces with polyhedral ones, Ann. of Math. 61 (1957), 456-483.
- [3]
- -, Decompositions of
, Topology of -Manifolds and Related Topics, ed. by M. K. Fort, Jr., Prentice-Hall, Englewood Cliffs, N. J., 1962.
- [4]
- -, Approximating surfaces from the side, Ann. of Math. 77 (1963), 145-192. MR 0150744 (27:731)
- [5]
- S. S. Cairns, Introductory topology, Ronald Press, New York, 1961. MR 0119198 (22:9964)
- [6]
- M. L. Curtis, Self-linked subgroups of semigroups, Amer. J. Math. 81 (1959), 889-892. MR 0108552 (21:7268)
- [7]
- C. H. Edwards, Concentricity in
-manifolds, Trans. Amer. Math. Soc. 113 (1964), 406-423. MR 0178459 (31:2716)
- [8]
- D. W. Henderson, Self-unlinked simple closed curves, Trans. Amer. Math. Soc. 120(1965) 470-480. MR 0187234 (32:4687)
- [9]
- -, Relative general position, Pacific J. Math. (to appear). MR 0200933 (34:819)
- [10]
- E. E. Moise, Affine structures in
-manifolds. V. The triangulation theorem and Hauptvermutung, Ann. of Math. 56 (1952), 96-114. MR 0048805 (14:72d)
- [11]
- C. D. Papakyriakopoulos, On solid tori, Proc. London Math. Soc. (3) 7 (1957), 281. MR 0087944 (19:441d)
- [12]
- -, Dehn's Lemma and asphericity of knots, Ann. of Math. 66 (1957), 1-26. MR 0090053 (19:761a)
- [13]
- H. Seifert and W. Threlfall, Lehrbuch der Topologie, Teubner, Leipzig, 1934.
- [14]
- A. Shapiro and J. H. C. Whitehead, A proof and extension of Dehn's Lemma, Bull. Amer. Math. Soc. 64 (1958), 174-178. MR 0103474 (21:2242)
- [15]
- J. Stallings, On the loop theorem, Ann. of Math. 72 (1960), 12-19. MR 0121796 (22:12526)
- [16]
- -, The piece-wise linear structures in Euclidean space, Proc. Cambridge Philos. Soc. 58 (1962), 481-188.
- [17]
- J. H. C. Whitehead, Simplicial spaces, nuclei and
-groups, Proc. London Math. Soc 45 (1939), 243-327.
- [18]
- -, Note on manifolds, Quart. J. Math. Oxford Ser. 12 (1941), 26-29. MR 0004781 (3:60h)
- [19]
- E. C. Zeeman, Relative simplicial approximation, Proc. Cambridge Philos. Soc. 60 (1964), 39-43. MR 0158403 (28:1626)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1965-0187233-0
PII:
S 0002-9947(1965)0187233-0
Article copyright:
© Copyright 1965 American Mathematical Society
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