Involutive Heegaard Floer homology and plumbed three-manifolds
arXiv:1704.02020
Abstract
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.
35 pages; corrected the statement of Lemma 7.1 and the proof of Theorem 7.2; final version, to appear in J. Inst. Math. Jussieu