Knots prime on many strings
HTML articles powered by AMS MathViewer
- by Steven A. Bleiler PDF
- Trans. Amer. Math. Soc. 282 (1984), 385-401 Request permission
Abstract:
A study is made of the factorization of prime knots into tangles. Several infinite families of knots which do not factor into prime tangles are examined, and a new characterization of knot primality is developed.References
- Joan S. Birman, F. González-Acuña, and José M. Montesinos, Heegaard splittings of prime $3$-manifolds are not unique, Michigan Math. J. 23 (1976), no. 2, 97–103. MR 431175 F. Bonahon and L. Siebenmann, New geometric splittings of classical knots (to appear).
- J. H. Conway, An enumeration of knots and links, and some of their algebraic properties, Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967) Pergamon, Oxford, 1970, pp. 329–358. MR 0258014
- M. J. Dunwoody and A. Pietrowski, Presentations of the trefoil group, Canad. Math. Bull. 16 (1973), 517–520. MR 404463, DOI 10.4153/CMB-1973-084-8 W. Jaco, Lectures on $3$-manifolds topology, CBMS Regional Conf. Ser. in Math., no. 43, Amer. Math. Soc., Providence, R. I., 1979.
- Robion C. Kirby and W. B. Raymond Lickorish, Prime knots and concordance, Math. Proc. Cambridge Philos. Soc. 86 (1979), no. 3, 437–441. MR 542689, DOI 10.1017/S0305004100056280
- W. B. Raymond Lickorish, Prime knots and tangles, Trans. Amer. Math. Soc. 267 (1981), no. 1, 321–332. MR 621991, DOI 10.1090/S0002-9947-1981-0621991-2 W. Menasco, Incompressible surfaces in the complement of alternating knots and links (preprint).
- José M. Montesinos, Seifert manifolds that are ramified two-sheeted cyclic coverings, Bol. Soc. Mat. Mexicana (2) 18 (1973), 1–32 (Spanish). MR 341467 —, Revêtements ramifies de noeuds espaces fibres de Seifert et scidements de Heegaard, Conferences, 1976, Orsay. F. H. Norwood, One-relator knots, Ph. D. Dissertation, University of Southwestern Louisiana, 1979.
- Kenneth A. Perko Jr., On $10$-crossing knots, Portugal. Math. 38 (1979), no. 1-2, 5–9 (1982). MR 682350
- Dale Rolfsen, Knots and links, Mathematics Lecture Series, No. 7, Publish or Perish, Inc., Berkeley, Calif., 1976. MR 0515288 M. Scharlemann, Tunnel number one knots are doubly prime (preprint).
- Horst Schubert, Knoten und Vollringe, Acta Math. 90 (1953), 131–286 (German). MR 72482, DOI 10.1007/BF02392437 D. Seal, Combinatorial double branched covers (to appear). L. Siebenmann, Exercises sur les noeuds rationnels, Orsay, 1975.
- Jonathan Simon, An algebraic classification of knots in $S^{3}$, Ann. of Math. (2) 97 (1973), 1–13. MR 310861, DOI 10.2307/1970874 W. Thurston, The geometry and topology of $3$-manifolds, Mimeographed Notes, Princeton University, 1978.
- Friedhelm Waldhausen, Gruppen mit Zentrum und $3$-dimensionale Mannigfaltigkeiten, Topology 6 (1967), 505–517 (German). MR 236930, DOI 10.1016/0040-9383(67)90008-0
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 282 (1984), 385-401
- MSC: Primary 57M25; Secondary 57M12, 57N10
- DOI: https://doi.org/10.1090/S0002-9947-1984-0728719-9
- MathSciNet review: 728719