We show that a decorated knot concordance $\mathcal{ C}$ from $K_0$ to $K_1$ induces an $\mathbb{ F}[U]$-module homomorphism \[G_{ \mathcal{ C}}: HFK^{ -}(-S^3,K_0) \to HFK^{ -}(-S^3,K_1)\] which preserves the Alexander and absolute $\mathbb{ Z}_2$-Maslov gradings. Our construction generalizes the concordance maps induced on $\widehat{ HFK}$ studied by Juh\'asz and Marengon, but uses the description of $HFK^{ -}$ as a direct limit of maps between sutured Floer homology groups discovered by Etnyre, Vela-Vick, and Zarev.
Categories: math.GT