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Knots are determined by their complements
Authors:
C. McA. Gordon and J. Luecke
Journal:
J. Amer. Math. Soc. 2 (1989), 371-415
MSC:
Primary 57M25; Secondary 57M40
MathSciNet review:
965210
Full-text PDF Free Access
References |
Similar Articles |
Additional Information
- [CGLS]
Marc
Culler, C.
McA. Gordon, J.
Luecke, and Peter
B. Shalen, Dehn surgery on knots, Ann. of Math. (2)
125 (1987), no. 2, 237–300. MR 881270
(88a:57026), http://dx.doi.org/10.2307/1971311
- [Cerf]
Jean
Cerf, Sur les difféomorphismes de la sphère de
dimension trois (Γ₄=0), Lecture Notes in Mathematics, No.
53, Springer-Verlag, Berlin, 1968 (French). MR 0229250
(37 #4824)
- [FW]
C.
D. Feustel and Wilbur
Whitten, Groups and complements of knots, Canad. J. Math.
30 (1978), no. 6, 1284–1295. MR 511562
(80b:57004), http://dx.doi.org/10.4153/CJM-1978-105-0
- [Ga]
David
Gabai, Foliations and the topology of 3-manifolds. III, J.
Differential Geom. 26 (1987), no. 3, 479–536.
MR 910018
(89a:57014b)
- [Gl]
Leon
Glass, A combinatorial analog of the Poincaré index
theorem, J. Combinatorial Theory Ser. B 15 (1973),
264–268. MR 0327558
(48 #5900)
- [J]
Klaus
Johannson, Équivalences d’homotopie des
variétés de dimension 3, C. R. Acad. Sci. Paris
Sér. A-B 281 (1975), no. 23, Ai,
A1009–A1010 (French). MR 0391096
(52 #11918)
- [L]
R.
A. Litherland, Surgery on knots in solid tori. II, J. London
Math. Soc. (2) 22 (1980), no. 3, 559–569. MR 596334
(82d:57002), http://dx.doi.org/10.1112/jlms/s2-22.3.559
- [T]
Heinrich
Tietze, Über die topologischen Invarianten mehrdimensionaler
Mannigfaltigkeiten, Monatsh. Math. Phys. 19 (1908),
no. 1, 1–118 (German). MR
1547755, http://dx.doi.org/10.1007/BF01736688
- [W]
Friedhelm
Waldhausen, Recent results on sufficiently large 3-manifolds,
Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ.,
Stanford, Calif., 1976), Part 2, Proc. Sympos. Pure Math., XXXII, Amer.
Math. Soc., Providence, R.I., 1978, pp. 21–38. MR 520520
(80e:57010)
-
- [CGLS]
- M. Culler, C. McA. Gordon, J. Luecke, and P. B. Shalen, Dehn surgery on knots, Ann. of Math. (2) 125 (1987), 237-300. MR 881270 (88a:57026)
- [Cerf]
- J. Cerf, Sur les diffeomorphismes de la sphère de dimension trois
 , Lecture Notes in Math., no. 53, Springer-Verlag, Berlin and New York, 1968. MR 0229250 (37:4824) - [FW]
- C. D. Feustel and W. Whitten, Groups and complements of knots, Canad. J. Math. 30 (1978), 1284-1295. MR 511562 (80b:57004)
- [Ga]
- D. Gabai, Foliations and the topology of
 -manifolds. III, J. Differential Geom. 26 (1987), 479-536. MR 910018 (89a:57014b) - [Gl]
- L. Glass, A combinatorial analog of the Poincaré Index Theorem, J. Combin. Theory Ser. B 15 (1973), 264-268. MR 0327558 (48:5900)
- [J]
- K. Johannson, Equivalences d'homotopie des variétés de dimension 3, C. R. Acad. Sci. Paris Sér. A 281 (1975), 1009-1010. MR 0391096 (52:11918)
- [L]
- R. A. Litherland, Surgery on knots in solid tori, II, J. London Math. Soc. (2) 22 (1980), 559-569. MR 596334 (82d:57002)
- [T]
- H. Tietze, Über die topologischen Invarianten mehrdimensionaler Mannigfaltigkeiten, Monatsh. Math. Phys. 19 (1908), 1-118. MR 1547755
- [W]
- F. Waldhausen, Recent results on sufficiently large
 -manifolds, Proc. Sympos. Pure Math., Vol. 32, Part 2, Amer. Math. Soc., Providence, RI, 1978, pp. 21-38. MR 520520 (80e:57010)
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Additional Information
C. McA. Gordon
Affiliation:
J. Luecke
Affiliation:
DOI:
http://dx.doi.org/10.1090/S0894-0347-1989-0965210-7
PII:
S 0894-0347(1989)0965210-7
Article copyright:
© Copyright 1989 American Mathematical Society
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