Volume 17, issue 6 (2017)

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Quasistabilization and basepoint moving maps in link Floer homology

Ian Zemke

Algebraic & Geometric Topology 17 (2017) 3461–3518

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.

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Heegaard Floer homology, knot invariants, link invariants
Mathematical Subject Classification 2010
Primary: 57M25, 57M27, 57R58
Received: 3 June 2016
Revised: 10 October 2016
Accepted: 14 November 2016
Published: 4 October 2017
Ian Zemke
Department of Mathematics
University of California, Los Angeles
520 Portola Plaza
Los Angeles, CA 90025
United States