# zbMATH — the first resource for mathematics

Prime knots and tangles. (English) Zbl 0472.57004

##### MSC:
 57M25 Knots and links in the $$3$$-sphere (MSC2010)
##### Keywords:
prime knots; tangles; prime tangle
Full Text:
##### References:
 [1] F. Bonahon (to appear). [2] 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. [3] J. C. Gómez Larrańaga, Knot primeness, Doctoral Dissertation, Cambridge University, 1981. [4] Richard E. Goodrick, Non-simplicially collapsible triangulations of \?$$^{n}$$, Proc. Cambridge Philos. Soc. 64 (1968), 31 – 36. · Zbl 0179.52602 [5] Jean-Claude Hausmann , Knot theory, Lecture Notes in Mathematics, vol. 685, Springer-Verlag, Berlin-New York, 1978. [6] A. Hatcher and W. Thurston, Incompressible surfaces in $$2$$-bridge knot complements (to appear). · Zbl 0602.57002 [7] William Jaco, Lectures on three-manifold topology, CBMS Regional Conference Series in Mathematics, vol. 43, American Mathematical Society, Providence, R.I., 1980. · Zbl 0433.57001 [8] Klaus Johannson, Homotopy equivalences of 3-manifolds with boundaries, Lecture Notes in Mathematics, vol. 761, Springer, Berlin, 1979. · Zbl 0412.57007 [9] Paik Kee Kim and Jeffrey L. Tollefson, Splitting the PL involutions of nonprime 3-manifolds, Michigan Math. J. 27 (1980), no. 3, 259 – 274. · Zbl 0458.57026 [10] Rob Kirby, Problems in low dimensional manifold theory, Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976) Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc., Providence, R.I., 1978, pp. 273 – 312. · Zbl 0394.57002 [11] Robion C. Kirby and W. B. Raymond Lickorish, Prime knots and concordance, Math. Proc. Cambridge Philos. Soc. 86 (1979), no. 3, 437 – 441. · Zbl 0426.57001 [12] Charles Livingston, Homology cobordisms of 3-manifolds, knot concordances, and prime knots, Pacific J. Math. 94 (1981), no. 1, 193 – 206. · Zbl 0472.57003 [13] W. Menasco, Incompressible surfaces in the complement of alternating knots and links (to appear). · Zbl 0525.57003 [14] K. A. Perko, A weak $$2$$-bridged knot with at most three bridges is prime, Notices Amer. Math. Soc. 26 (1978), A-648 (and a preprint). [15] -, Invariants of eleven-crossing knots (to appear). [16] Horst Schubert, Über eine numerische Knoteninvariante, Math. Z. 61 (1954), 245 – 288 (German). · Zbl 0058.17403 [17] Friedhelm Waldhausen, Über Involutionen der 3-Sphäre, Topology 8 (1969), 81 – 91 (German). · Zbl 0185.27603
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.