Generators of certain groups of semi-free \(S^ 1\) actions on spheres and splitting of codimension-3 knot exact sequences (Q582644)

This paper studies the group \(\Sigma^ n_ k(S^ 1)\) of oriented equivariant diffeomorphism classes of smooth semi-free \(S^ 1\) actions on oriented homotopy \((n+2k-1)\)-spheres with fixed set \(S^{n-1}\) having trivial complex normal bundle. The group operation is connected sum. The author defines a homomorphism into the integers if \(n>2k\), and using this shows that Brieskorn spheres with natural actions give either a generator or twice a generator when the group has rank 1.