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Rank inequalities for the Heegaard Floer homology of Seifert homology spheres


Authors: Çağrı Karakurt and Tye Lidman
Journal: Trans. Amer. Math. Soc. 367 (2015), 7291-7322
MSC (2010): Primary 57R58, 57M27
DOI: https://doi.org/10.1090/S0002-9947-2014-06451-9
Published electronically: December 23, 2014
MathSciNet review: 3378830
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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 $ \vert\deg f\vert\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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Additional Information

Çağrı Karakurt
Affiliation: Department of Mathematics, The University of Texas at Austin, Austin, Texas 78712
Address at time of publication: Department of Mathematics, Bogazici University, Bebek-Istanbul, Turkey 34342
Email: cagri.karakurt@boun.edu.tr

Tye Lidman
Affiliation: Department of Mathematics, The University of Texas at Austin, Austin, Texas 78712

DOI: https://doi.org/10.1090/S0002-9947-2014-06451-9
Keywords: Heegard Floer homology, Seifert homology sphere, graded root, numerical semigroup, degree, botany
Received by editor(s): October 9, 2013
Published electronically: December 23, 2014
Article copyright: © Copyright 2014 American Mathematical Society