Triple linking numbers and Heegaard Floer homology

Eugene, Gorsky,; Lidman, Tye; Liu, Beibei; Moore, Allison H.

doi:10.48550/arxiv.2006.15484

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2020

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“…Link Floer homology was known to detect the trivial 1 n-braid together with its braid axis [2] and determine if a link is split [29]. It was also known that a stronger version of link Floer homology CFL ∞ detects the Borromean rings and the Whitehead link [8].…”

Section: Introductionmentioning

confidence: 99%

Knot Floer homology, link Floer homology and link detection

Binns,

Martin

2020

Preprint

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We give new link detection results for knot and link Floer homology inspired by recent work on Khovanov homology. We show that knot Floer homology detects T (2, 4), T (2, 6), T (3, 3), L7n1, and the link T (2, 2n) with the orientation of one component reversed. We show link Floer homology detects T (2, 2n) and T (n, n), for all n. Additionally we identify infinitely many pairs of links such that both links in the pair are each detected by link Floer homology but have the same Khovanov homology and knot Floer homology. Finally, we use some of our knot Floer detection results to give topological applications of annular Khovanov homology.

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Section: Introductionmentioning

confidence: 99%