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Floer homology, clasp-braids and detection results

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arxiv 2405.11224 v1 pith:BYT3RSXG submitted 2024-05-18 math.GT

Fraser Binns , Subhankar Dey This is my paper · ORCID
classification math.GT
keywords homologyfloerlinkdetectiondetectskhovanovresultresults
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abstract

Martin showed that link Floer homology detects braid axes. In this paper we extend this result to give a topological characterisation of links which are almost braided from the point of view of link Floer homology. The result is inspired by work of Baldwin-Sivek and Li-Ye on nearly fibered knots. Applications include that Khovanov homology detects the Whitehead link and $L7n2$, as well as infinite families of detection results for link Floer homology and annular Khovanov homology.

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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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