Concordance maps in HFK−

Abstract

We show that a decorated knot concordance [Formula: see text] from [Formula: see text] to [Formula: see text] induces an [Formula: see text]-module homomorphism [Formula: see text] which preserves the Alexander and absolute [Formula: see text]-Maslov gradings. Our construction generalizes the concordance maps induced on [Formula: see text] studied by Juhász and Marengon [Concordance maps in knot Floer homology, Geom. Topol. 20 (2016) 3623–3673], but uses the description of [Formula: see text] 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].