Rank inequalities for the Heegaard Floer homology of Seifert homology spheres

Cagri Karakurt; Tye Lidman

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arXiv · 1310.0760

Rank inequalities for the Heegaard Floer homology of Seifert homology spheres

Cagri Karakurt·Tye Lidman

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Abstract

We establish three rank inequalities for the reduced flavor of Heegaard Floer homology of Seifert fibered integral homology spheres. Combining these inequalities with the known classifications of non-zero degree maps between Seifert fibered spaces, we prove that a map f from Y' to Y between Seifert homology spheres yields the inequality that |deg f| rank HFred(Y) is at most rank HFred(Y'). These inequalities are also applied in conjunction with an algorithm of Nemethi to give a method to solve the botany problem for the Heegaard Floer homology of these manifolds.

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BibTeX RIS

Cagri Karakurt, Tye Lidman. 2013-10-02. Rank inequalities for the Heegaard Floer homology of Seifert homology spheres. https://arxiv.org/abs/1310.0760

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