## A characterization of 2-knots groups.(English)Zbl 0822.57018

In 1925 E. Artin characterised 1-knot groups in terms of their presentations, and in 1965 M. Kervaire gave an intrinsic algebraic characterisation of $$n$$-knot groups ($$n \geq 3$$). This paper characterises 2-knot groups in the spirit of Artin, using a proper embedding of a surface in $$S^ 3 \times [-1, 1]$$ constructed by means of closed braids associated with the presentation.
A generalisation to embeddings of surfaces in $$S^ 4$$ is also given.
Reviewer: C.Kearton (Durham)

### MSC:

 57Q45 Knots and links in high dimensions (PL-topology) (MSC2010)

### Keywords:

2-knot groups; closed braids; presentation
Full Text: