Heegaard Floer homology and several families of Brieskorn spheres

Abstract

In Ozsváth and Szabó (2003) [15] the authors gave a combinatorial description for the Heegaard Floer homology of boundaries of certain negative-definite plumbings. Némethi constructed a remarkable algorithm in Némethi (2005) [12] for executing these computations for almost-rational plumbings, and his work in Némethi (2007) [13] 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 in Borodzik and Némethi (2011) [3]. We also compute HF+ for the families −Σ(2,5,k) and −Σ(2,7,k).