Involutive Heegaard Floer homology and plumbed three-manifolds

摘要

We compute the involutive Heegaard Floer homology of the family ofthree-manifolds obtained by plumbings along almost-rational graphs. (Thisincludes all Seifert fibered homology spheres.) We also study the involutiveHeegaard Floer homology of connected sums of such three-manifolds, andexplicitly determine the involutive correction terms in the case that all ofthe summands have the same orientation. Using these calculations, we give a newproof of the existence of an infinite-rank subgroup in the three-dimensionalhomology cobordism group.