论文信息 - Groups and Complements of Knots

Groups and Complements of Knots

We investigate the extent to which knot groups determine knot manifolds and knot types. Let Ki(i = 1, 2) denote a tame knot in S3, let Ci denote a Ki-knot manifold, and assume that Π1 (C1) ≈ Π 1(C2). The first named author recently showed (in [6]) that, if C1 has no essential annulus, then C1 ≅ C2, and so K1 and K2 are equivalent, if K1 has property P.

C. Feustel | W. Whitten

[1] C. Feustel. On the torus theorem and its applications , 1976 .

[2] W. Whitten. Algebraic and geometric characterizations of knots , 1974 .

[3] G. P. Scott. On sufficiently large 3-manifolds , 1972 .

[4] C. Feustel. A splitting theorem for closed orientable 3-manifolds , 1972 .

[5] John Stallings,et al. Group Theory and Three-dimensional Manifolds , 1971 .

[6] F. Waldhausen. Gruppen mit Zentrum und 3-dimensionale Mannigfaltigkeiten , 1967 .

[7] D. Noga. Über den Außenraum von Produktknoten und die Bedeutung der Fixgruppen , 1967 .

[8] J. Simon. On the problems of determining knots by their complements and knot complements by their groups , 1976 .

[9] R. Bing,et al. Cubes with knotted holes , 1971 .

[10] Horst Schubert,et al. Die eindeutige Zerlegbarkeit eines Knotens in Primknoten , 1949 .