Simple knots in compact, orientable 3-manifolds

Transactions of the American Mathematical Society

Volumn 273, Issue 1, 1982, Pages 75-91

  Myers, Robert ^a  

^a OKLAHOMA STATE UNIVERSITY   (United States)

Author keywords

3 manifold; Hyperbolic 3 manifold; Knot; Knot group; Poincare Conjecture; Semisimple 3 manifold; Simple 3 manifold; Simple knot

Indexed keywords

EID: 33646912413     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-1982-0664030-0     Document Type: Article

References (21)

1. R. H. Bing, Necessary and sufficient conditions that a 3-manifold he Ann. of Math. 68 (1958), 17-37.
2. R. H. Fox, Recent development of knot theory at Princeton, Proc. Internat. Congress Math., Cambridge, Mass., 1950, Amer. Math. Soc., Providence, R. I., pp. 453-457.
3. W. Haken, Some results on surfaces in 3-manifolds, Studies in Modern Topology, Prentice-Hall, Englewood Cliffs, N. J., 1968, pp. 39-98.
4. J. Hempel, 3-manifolds, Ann. of Math. Studies, no. 86, Princeton Univ. Press, Princeton, N. J., 1976.
5. W. Jaco, Three-manifolds with fundamental group a free product. Bull. Amer. Math. Soc. 75 (1969), 972-977.
6. W. Jaco, Lectures on three-manifold topology, CBMS Regional Conference Series in Math. No. 43, Amer. Math. Soc., Providence, R. I., 1980.
7. W. Jaco and R. Myers, An algebraic determination of closed, orientable 3-manifolds, Trans. Amer. Math. Soc. 253 (1979), 149-170.
8. W. Jaco and P. Shalen, Seifert fibered spaces in 3-manifolds, Mem. Amer. Math. Soc. No. 220 (1979).
9. K. Johannson, Homotopy equivalences of 3-manifolds with boundaries. Lecture Notes in Math., vol. 761, Springer-Verlag, Berlin and New York, 1979.
10. D. R. McMillan, On homologically trivial 3-manifolds, Trans. Amer. Math. Soc., 98 (1961), 350-367.
11. J. Milnor, A unique factorization theorem for 3-manifolds, Amer. J. Math. 84 (1962), 1-7.
12. pKnots, Groups, and 3-Manifolds, Ann. of Math. Studies, no. 84, Princeton Univ. Press, Princeton, N. J., 1975, pp. 227-260.
13. R. Myers, Homology cohordisms, link concordances, and hyperbolic 3-manifolds (preprint).
14. W. H. Row, An algebraic characterization of connected sum factors of closed 3-manifolds, Trans. Amer. Math. Soc. 250 (1979), 347-356.
15. H. Schubert, Knoten und Vollringe, Acta. Math. 90 (1953), 131-286.
16. H. Seifert, Schlingknoten, Math. Z. 52 (1949), 62-80.
17. W. Thurston, The geometry and topology of 3-manifolds, lecture notes, Princeton.
18. F. Waldhausen, Eine Klasse von 3-dimensionalen Mannigfaltigkeiten. I, II, Invent. Math. 3 (1967), 308-333.
19. F. Waldhausen, Invent. Math 4 (1967), 87-117.
20. F. Waldhausen, On irreducible 3-manifolds which are sufficiently large, Ann. of Math. (2) 87 (1968), 56-88.
21. W. Whitten, Groups and manifolds characterizing links. Knots, Groups, and 3-Manifolds, Ann. of Math. Studies, no. 84, Princeton Univ. Press, Princeton, N. J., 1975, pp. 63-86.