Juxin Yang: Introduction to Selick–Wu's $A^{min}$-theory

Abstract: How much of a loop space can be recovered from its homology? Selick–Wu's \(A^{\mathrm{min}}\)-theory turns natural coalgebra decompositions of tensor coalgebras into functorial splittings of looped suspensions. I will introduce this theory and explain how it reveals attaching maps in the fibers of pinch maps for two-cell complexes, enabling homotopy group computations beyond the metastable range. A concrete highlight is the computation of the 2-primary component of \(\pi_{18}(\Sigma^3\mathbb{C}P^2)\). I will conclude with motivic analogues, including an odd-primary splitting of looped motivic spheres.