Quasistabilization and basepoint moving maps in link Floer homology

Zemke, Ian

doi:10.2140/agt.2017.17.3461

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Quasistabilization and basepoint moving maps in link Floer homology

Ian Zemke

Algebraic & Geometric Topology 17 (2017) 3461–3518

DOI: 10.2140/agt.2017.17.3461

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 ${CFL}_{U V}^{\infty}$ . 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.

Keywords

Heegaard Floer homology, knot invariants, link invariants

Mathematical Subject Classification 2010

Primary: 57M25, 57M27, 57R58

References

Publication

Received: 3 June 2016

Revised: 10 October 2016

Accepted: 14 November 2016

Published: 4 October 2017

Authors

Ian Zemke
Department of Mathematics University of California, Los Angeles 520 Portola Plaza Los Angeles, CA 90025 United States

Volume 17, issue 6 (2017)