Spin(4) actions on 8-dimensional manifolds. I (Q1567030)

We study smooth Spin(4) actions on closed, orientable 8-dimensional manifolds, where Spin(4) is isomorphic to the group \(\text{SU}(2) \times \text{SU}(2)\). We examine the isotropy structures that can arise, and give an equivariant classification in the case where the set of exceptional orbits, stabilized by finite-cyclic groups, is empty.