Stably irreducible surfaces in \(S^ 4\) (Q2266269)

Working in the smooth category, a surface F embedded in \(S^ 4\) is irreducible if it is not the connected sum of an unknotted torus and an embedded surface. It is stably irreducible if no connected sum of F with a number of unknotted tori is diffeomorphic to the connected sum of a surface of lower genus with a number of unknotted tori. Using a construction of a spun torus, analogous to the construction of a spun knot, the author produces examples of stably irreducible surfaces in \(S^ 4\), of arbitrary genus, whose complements have fundamental groups isomorphic to classical knot groups.