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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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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