Algebraic & Geometric Topology

Quasistabilization and basepoint moving maps in link Floer homology

Ian Zemke

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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

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

Received: 3 June 2016
Revised: 10 October 2016
Accepted: 14 November 2016
First available in Project Euclid: 16 November 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds 57R58: Floer homology

Heegaard Floer homology knot invariants link invariants


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.

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