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Links of Second Smallest Knot Floer Homology

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arxiv 2011.11810 v1 pith:OR56UUV6 submitted 2020-11-24 math.GT

Juhyun Kim This is my paper · ORCID
classification math.GT
keywords floerhomologyknotlinksproveranksecondsmallest
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We prove that the rank of knot Floer homology detects the Hopf links, and generalize this result further to classify the links of the second smallest knot Floer homology. We also prove a knot Floer homology analog of arXiv:1910.04246v1 [math.GT] and give a partial answer to when the equality holds in the rank inequality between the knot Floer homology of a link and its sublinks.

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  1. On Heegaard Floer minimal knots in sutured manifolds

    math.GT 2025-05 conditional novelty 7.0 of 10

    A rank-minimality condition in sutured Heegaard Floer homology forces a connect-sum decomposition with a Floer simple knot, and link Floer homology detects spherical braid closures in S^1×S^2.

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