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A characterization of 2-knots groups.

Francisco González-Acuña (1994)

Revista Matemática Iberoamericana

A n-knot group is the fundamental group of the complement of an n-sphere smoothly embedded in Sn+2. Artin gave in 1925 ([A]) an algebraic characterization of 1-knot groups. M. Kervaire gave in 1965 ([K]) an algebraic characterization of n-knot groups for n ≥ 3. The problem of characterizing algebraically 2-knot groups has been posed several times (see for example [Su, Problem 4.7]). Ribbon 2-knot groups have been characterized algebraically by Yajima [Y].We will give here a characterization of 2-knot...

Alexander ideals of classical knots.

Cherry Kearton, Stephen M. J. Wilson (1997)

Publicacions Matemàtiques

The Alexander ideals of classical knots are characterised, a result which extends to certain higher dimensional knots.

An unknotting theorem for tori in 4-dimensional spheres.

Akiko Shima (1998)

Revista Matemática Complutense

Let T be a torus in S4 and T* a projection of T. If the singular set Gamma(T*) consists of one disjoint simple closed curve, then T can be moved to the standard position by an ambient isotopy of S4.

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