Rank inequalities for the Heegaard Floer homology of Seifert homology spheres

Karakurt, Çağrı; Lidman, Tye

doi:10.1090/S0002-9947-2014-06451-9

Rank inequalities for the Heegaard Floer homology of Seifert homology spheres
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by Çağrı Karakurt and Tye Lidman PDF

Trans. Amer. Math. Soc. 367 (2015), 7291-7322 Request permission

Abstract:

We establish three rank inequalities for the reduced flavor of Heegaard Floer homology of Seifert fibered integer homology spheres. Combining these inequalities with the known classifications of non-zero degree maps between Seifert fibered spaces, we prove that a map $f:Y’ \to Y$ between Seifert homology spheres yields the inequality $|\deg f|\mathrm {rank} HF_{\mathrm {red}}(Y) \leq \mathrm {rank} HF_{\mathrm {red}}(Y’)$. These inequalities are also applied in conjunction with an algorithm of Némethi to give a method to solve the botany problem for the Heegaard Floer homology of these manifolds.

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