Commutative comultiplications on the localizations of a wedge sum of spheres and Moore spaces

Abstract

Let $\mathcal{P}$ be a collection of prime numbers and let $M(G,n)$ be the Moore space of type $(G,n)$, where $G$ is a finitely generated abelian group and $n$ is a positive integer. This paper focuses on the homotopy commutative comultiplication structures on the localization $X_{\mathcal{P}}$ of a wedge $X: = \mathbb S^m \vee M(G,n)$ of the $m$-spheres and Moore spaces for $2 \leq m < n$. A list of examples is provided for examination of the phenomena of commutative comultiplications on $X_{\mathcal{P}}$ up to homotopy.