Quasi-stabilization and basepoint moving maps in link Floer homology

TL;DR

This paper studies how adding, removing, and moving basepoints affect link Floer homology, introducing quasi-stabilization and a calculus for basepoint movements, and proves a conjecture about finger moves.

Contribution

It establishes that quasi-stabilization is a natural operation on $CFL_{UV}^ Infty$ and develops a simple calculus for basepoint movements, proving a conjecture of Sarkar.

Findings

Quasi-stabilization is a natural operation on link Floer homology.

Developed a calculus for moving basepoints on link Floer complexes.

Proved Sarkar's conjecture about the map induced by finger moves.

Abstract

We analyze the effect of adding, removing, and moving basepoints on link Floer homology. We prove that adding or removing basepoints via a procedure called quasi-stabilization is a natural operation on a certain version of link Floer homology, which we call $CFL_{UV}^\infty$. We consider the effect on the full link Floer complex of moving basepoints, and develop a simple calculus for moving basepoints on the link Floer complexes. We apply it to compute the effect of several diffeomorphisms corresponding to moving basepoints. Using these techniques we prove a conjecture of Sarkar about the map on the full link Floer complex induced by a finger move along a link component.