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Keyword: Transonic Flutter (2)	31 Mar 2025	Run
Keyword: Sutured Manifolds (1)	31 Mar 2025	Run
Keyword: Life Therapeutics (3)	31 Mar 2025	Run
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articleNo Access
Concordance maps in HFK $^{-}$
- Lev Tovstopyat-Nelip
Journal of Knot Theory and Its Ramifications01 Apr 2022
Preview Abstract
We show that a decorated knot concordance $𝒞$ from $K_{0}$ to $K_{1}$ induces an $𝔽 [U]$ -module homomorphism
$G_{𝒞} : {HFK}^{-} (- S^{3}, K_{0}) \to {HFK}^{-} (- S^{3}, K_{1}),$
which preserves the Alexander and absolute $ℤ_{2}$ -Maslov gradings. Our construction generalizes the concordance maps induced on $\hat{HFK}$ studied by Juhász and Marengon [Concordance maps in knot Floer homology, Geom. Topol.20 (2016) 3623–3673], but uses the description of ${HFK}^{-}$ as a direct limit of maps between sutured Floer homology groups discovered by Etnyre et al. [Sutured Floer homology and invariants of Legendrian and transverse knots, Geom. Topol.21 (2017) 1469–1582].

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