Quasi-stabilization and basepoint moving maps in link Floer homology
By Ian Zemke. 2016
54 citations recorded by the source corpus.
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.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2d0d94edfb87c46f357935eebd58ae17867a8b5f
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Connected sums and involutive knot Floer homology (2017, methodology): “The diffeomorphism map ρ∗ is considered in [33, 37].”
- Knot Floer homology obstructs ribbon concordance (2019, unknown): “st. Note that composition with a grading preserving automorphism does not aect the statement of Theorem1.1. The basepoint moving automorphism map has been studied by Sarkar [Sar15] and by the author [Zem17]. Next, we discuss gradings. If L is a null-homologous link in Y (i.e. the total class of L va”