The equivalence of lattice and Heegaard Floer homology

Abstract

We prove Némethi's conjecture: if $Y$ is a 3-manifold which is the boundary of a plumbing of a tree of disk bundles over $S^2$, then the lattice homology of $Y$ coincides with the Heegaard Floer homology of $Y$. We also give a conjectural description of the $H_1(Y)/\mathrm{Tors}$ action when $b_1(Y)>0$.

arXiv comment46 pages. v4 Revisions in response to referee reports. Accepted version, Duke Math. Journal