Heegaard Floer homology and several families of Brieskorn spheres

Abstract

Ozsváth and Szabó gave a combinatorial description for the Heegaard Floer homology of boundaries of certain negative-definite plumbings. Némethi constructed a remarkable algorithm for executing these computations for almost-rational plumbings, and his work gives a formula computing the invariants for the Brieskorn homology spheres -Σ (p,q,pqn + 1). Here we give a formula for HF^{+}(-Σ(p,q,pqn-1)), generalizing the one for the n=1 case given by Borodzik and Némethi. We also compute HF^{+} for the families -Σ(2,5,k) and -Σ(2,7,k).

Revisions in this version: corrected some citations in introduction; fixed signs in Corollary 3 and table in Remark 4; simplified some arguments in Section 3. This version is the published version