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In this paper we consider $4$-dimensional steady soliton singularity models,i.e., complete steady gradient Ricci solitons that arise as the rescaled limitof a finite time singular solution of the Ricci flow on a closed $4$-manifold.In particular, we study the geometry at infinity of such Ricci solitons underthe assumption that their tangent flow at infinity is the product of$\mathbb{R}$ with a $3$-dimensional spherical space form. We also classify thetangent flows at infinity of $4$-dimensional steady soliton singularity modelsin general.

Four-Dimensional Steady Gradient Ricci Solitons with $3$-Cylindrical Tangent Flows at Infinity