Moving basepoints and the induced automorphisms of link Floer homology

Abstract

Given an l-component pointed oriented link (L,p) in an oriented three-manifold Y, one can construct its link Floer chain complex CFL(Y,L,p) over the polynomial ring F_2[U_1,...,U_l]. Moving the basepoint p_i in the link component L_i once around induces an automorphism of CFL(Y,L,p). In this paper, we study an automorphism (a possibly different one) of CFL(Y,L,p) defined explicitly in terms of holomorphic disks; for links in S^3, we show that these two automorphisms are the same.

27 pages

References in corpus (5)

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• Connected sums and involutive knot Floer homology
• Hilbert schemes and $y$-ification of Khovanov-Rozansky homology
• Quasi-stabilization and basepoint moving maps in link Floer homology
• Graph cobordisms and Heegaard Floer homology
• Bordered Floer homology and existence of incompressible tori in homology spheres
• Concordance maps in knot Floer homology
• Duality and mapping tori in Heegaard Floer homology
• An enhanced Euler characteristic of sutured instanton homology
• Functoriality of the EH class and the LOSS invariant under Lagrangian concordances
• Projective Naturality in Heegaard Floer Homology
• Involutive Heegaard Floer homology and rational cuspidal curves
• On sums of torus knots concordant to alternating knots
• Tautological classes and symmetry in Khovanov-Rozansky homology
• Khovanov homology detects split links
• An involutive upsilon knot invariant
• Non-orientable link cobordisms and torsion order in Floer homologies
• Locally equivalent Floer complexes and unoriented link cobordisms
• New Heegaard Floer slice genus and clasp number bounds
• Correction to the article: Floer homology and splicing knot complements
• Unoriented Cobordism Maps on Link Floer Homology
• Knot surgery formulae for instanton Floer homology I: the main theorem
• 2-torsion in instanton Floer homology