A characterization of 2-knots

Autores: Francisco Javier González Acuña
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 10, Nº 2, 1994, págs. 221-228
Idioma: inglés
Títulos paralelos:
- Una caracterización de grupos de 2-anidaciones.
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Resumen
- 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 groups in terms of presentations. It has the flavor of Artin's characterization of 1-knot groups. S. Kamada has independently obtained another characterization of 2-knot groups ([Ka]).