Moving basepoints and the induced automorphisms of link Floer homology

Abstract

Given an $l$–component pointed oriented link $\left(L,p\right)$ in an oriented three-manifold $Y$, one can construct its link Floer chain complex $CFL\left(Y,L,p\right)$ over the polynomial ring ${\mathbb{F}}_2\left[U_1,\dots ,U_l\right]$. Moving the basepoint $p_i\in L_i$ once around the link component $L_i$ induces an automorphism of $CFL\left(Y,L,p\right)$. We study a (possibly different) automorphism of $CFL\left(Y,L,p\right)$ defined explicitly in terms of holomorphic disks; for links in $S^3$, we show that these two automorphisms are the same.