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arXiv · 1206.2558

Heegaard Floer homology and several families of Brieskorn spheres

Eamonn Tweedy
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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).

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Eamonn Tweedy. 2013-04-02. Heegaard Floer homology and several families of Brieskorn spheres. https://arxiv.org/abs/1206.2558

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