Rank inequalities for the Heegaard Floer homology of Seifert homology\n spheres

2013/10/02 by Çağrı Karakurt, Karakurt, Cagri, Tye Lidman +1
Mathematics · Medicine · #57M27 #57R58 #Advanced Operator Algebra Research #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1310.0760

openalex publication_date 2013/10/02 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Holomorphic disks and knot invariants
• Holomorphic disks and topological invariants for closed three-manifolds

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