Fibered 2-knots and lens spaces
Let \(M^ 0\) be a punctured 3-manifold, i.e. \(M^ 0\) is obtained from a 3-manifold M by removing an open 3-ball. The fibred 2-knot in \(S^ 4\) with fibre \(M^ 0\) is called an \(M^ 0\)-fibred 2-knot. The author determines possible \(M^ 0\)-fibred 2-knots in \(S^ 4\) for all M. In fact, he proves: Theorem. Let K be an \(M^ 0\)-fibred 2-knot in a homology 4-sphere \(\Sigma\). Then \(\Sigma \cong S^ 4\), and K is a connected sum of particular type of fibred 2-knots. As an application of the theorem, the author provides a counter-example to the 4-dimensional Smith conjecture.
scientific article; zbMATH DE number 4153485