Links with unlinking number one are prime
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- by C. McA. Gordon and J. Luecke PDF
- Proc. Amer. Math. Soc. 120 (1994), 1271-1274 Request permission
Abstract:
We prove that a link with unlinking number one is prime.References
- Mario Eudave Muñoz, Primeness and sums of tangles, Trans. Amer. Math. Soc. 306 (1988), no. 2, 773–790. MR 933317, DOI 10.1090/S0002-9947-1988-0933317-1
- C. McA. Gordon and J. Luecke, Only integral Dehn surgeries can yield reducible manifolds, Math. Proc. Cambridge Philos. Soc. 102 (1987), no. 1, 97–101. MR 886439, DOI 10.1017/S0305004100067086 —, Reducible manifolds and Dehn surgery (to appear).
- Paik Kee Kim and Jeffrey L. Tollefson, Splitting the PL involutions of nonprime $3$-manifolds, Michigan Math. J. 27 (1980), no. 3, 259–274. MR 584691
- W. B. Raymond Lickorish, The unknotting number of a classical knot, Combinatorial methods in topology and algebraic geometry (Rochester, N.Y., 1982) Contemp. Math., vol. 44, Amer. Math. Soc., Providence, RI, 1985, pp. 117–121. MR 813107, DOI 10.1090/conm/044/813107
- José M. Montesinos, Surgery on links and double branched covers of $S^{3}$, Knots, groups, and $3$-manifolds (Papers dedicated to the memory of R. H. Fox), Ann. of Math. Studies, No. 84, Princeton Univ. Press, Princeton, N.J., 1975, pp. 227–259. MR 0380802
- Martin G. Scharlemann, Unknotting number one knots are prime, Invent. Math. 82 (1985), no. 1, 37–55. MR 808108, DOI 10.1007/BF01394778
- Friedhelm Waldhausen, Über Involutionen der $3$-Sphäre, Topology 8 (1969), 81–91 (German). MR 236916, DOI 10.1016/0040-9383(69)90033-0
- Xingru Zhang, Unknotting number one knots are prime: a new proof, Proc. Amer. Math. Soc. 113 (1991), no. 2, 611–612. MR 1076582, DOI 10.1090/S0002-9939-1991-1076582-0
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 1271-1274
- MSC: Primary 57M25
- DOI: https://doi.org/10.1090/S0002-9939-1994-1195721-7
- MathSciNet review: 1195721