Recently constructed by Hendricks and Manolescu, involutive Heegaard Floer homology provides several new tools for studying the three-dimensional homology cobordism group. In this talk, we will describe the structure of the involutive Floer homology for certain connected sums of plumbed three-manifolds, and give some applications of these computations. In particular, we show that if Y is a connected sum of Seifert fibered spaces with Rokhlin invariant \mu(Y) = 1, then Y is not torsion in the homology cobordism group. This is joint work with Matthew Stoffregen.