  We compute the involutive Heegaard Floer homology of the family of
three-manifolds obtained by plumbings along almost-rational graphs. (This
includes all Seifert fibered homology spheres.) We also study the involutive
Heegaard Floer homology of connected sums of such three-manifolds, and
explicitly determine the involutive correction terms in the case that all of
the summands have the same orientation. Using these calculations, we give a new
proof of the existence of an infinite-rank subgroup in the three-dimensional
homology cobordism group.
