Heegaard Floer homology and several families of Brieskorn spheres

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 , p q n + 1 ) . Here we give a formula for HF + ( − Σ ( p , q , p q n − 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 ) .