On Heegaard Floer minimal knots in sutured manifolds

Fraser Binns

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arXiv · 2505.19268

On Heegaard Floer minimal knots in sutured manifolds

Fraser Binns

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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 $S^1\times S^2$, showing that link Floer homology detects spherical braid closures among homologically nontrivial links.

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Fraser Binns. 2026-07-01. On Heegaard Floer minimal knots in sutured manifolds. https://arxiv.org/abs/2505.19268

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