$S U(2)$-invariant steady gradient Ricci solitons on four-manifolds

Using center manifolds and topological degree theory, we construct a new family of complete, $SU(2)$-invariant and steady gradient Ricci solitons on the four-dimensional non-compact cohomogeneity one manifold with group diagram Z₄⊂ U(1)⊂ SU(2). We also provide simpler constructions of the existing $U(2)$-invariant steady and complete gradient solitons on the cohomogeneity one manifolds with group diagrams Zₙ⊂ U(1)⊂ SU(2) for any n∈ N, including Appleton's non-collapsed solitons for n≥ 3.