On Heegaard Floer minimal knots in sutured manifolds

2025/05/25 by Binns, Fraser
#57K31 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2505.19268

Abstract

Li-Xie-Zhang classified instanton Floer minimal knots in balanced sutured manifolds subject to a condition on the fundamental group. In this paper, we give a similar classification in the Heegaard Floer homology setting. Since our classifications agree when they are both applicable, this provides further evidence for the conjecture of Kronheimer-Mrowka that instanton Floer homology and Heegaard Floer homology are isomorphic. We also study link Floer homology botany question in S¹× S², showing that link Floer homology detects spherical braid closures among homologically nontrivial links.

Citations

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Related

• On Floer minimal knots in sutured manifolds
• Decomposing sutured monopole and Instanton Floer homologies
• Knots, sutures and excision
• Instanton and the depth of taut foliations
• Heegaard diagrams and Floer homology