2021/11/23 by Guanheng Chen, Chen, Guanheng
Mathematics · Medicine · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Botulinum Toxin and Related Neurological Disorders
paper · pdf · doi:10.48550/arxiv.2111.11891
In this note, we investigate homomorphisms from the periodic Floer homology (PFH) to the quantitative Heegaard Floer homology. We call the homomorphisms closed-open morphisms. Under certain assumptions on the Lagrangian link, we first follow R. Lipshitz's idea to give a cylindrical formulation of the quantitative Heegaard Floer homology. Then we construct the closed-open morphisms from the PFH to the quantitative Heegaard Floer homology. Moreover, we show that the morphisms are non-vanishing. As an application, we deduce a relation between the PFH-spectral invariants and the HF-spectral invariants.