## Algebraic & Geometric Topology

### Quasistabilization and basepoint moving maps in link Floer homology

Ian Zemke

#### 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 quasistabilization is a natural operation on a certain version of link Floer homology, which we call $CFLUV∞$. 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 17, Number 6 (2017), 3461-3518.

Dates
Revised: 10 October 2016
Accepted: 14 November 2016
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.agt/1510841513

Digital Object Identifier
doi:10.2140/agt.2017.17.3461

Mathematical Reviews number (MathSciNet)
MR3709653

Zentralblatt MATH identifier
06791655

#### Citation

Zemke, Ian. Quasistabilization and basepoint moving maps in link Floer homology. Algebr. Geom. Topol. 17 (2017), no. 6, 3461--3518. doi:10.2140/agt.2017.17.3461. https://projecteuclid.org/euclid.agt/1510841513