A characterization of 2-knots groups (Q1335454)

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.