Moving basepoints and the induced automorphisms of link Floer homology

TL;DR

This paper investigates automorphisms of link Floer chain complexes induced by moving basepoints and shows their equivalence to automorphisms defined via holomorphic disks for links in S^3.

Contribution

It explicitly compares automorphisms from basepoint movement with those from holomorphic disk counts in link Floer homology, establishing their equivalence in S^3.

Findings

Automorphisms from basepoint movement and holomorphic disks are equivalent in S^3.

Provides an explicit description of automorphisms in terms of holomorphic disks.

Enhances understanding of symmetries in link Floer homology.

Abstract

Given an l-component pointed oriented link (L,p) in an oriented three-manifold Y, one can construct its link Floer chain complex CFL(Y,L,p) over the polynomial ring F_2[U_1,...,U_l]. Moving the basepoint p_i in the link component L_i once around induces an automorphism of CFL(Y,L,p). In this paper, we study an automorphism (a possibly different one) of CFL(Y,L,p) defined explicitly in terms of holomorphic disks; for links in S^3, we show that these two automorphisms are the same.