## 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.## References

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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
- MR Author ID: 808881
- Received by editor(s): October 9, 2013
- Published electronically: December 23, 2014
- © Copyright 2014 American Mathematical Society
- 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
- MathSciNet review: 3378830