2007/06/05 by Lawrence P. Roberts, Roberts, Lawrence P.
Mathematics · Medicine · #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.0706.0743
openalex publication_date 2007/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A companion paper to "On knot Floer homology in branched double covers" applied to braided branched loci. We reprove the main result of that paper concerning alternating branched loci when projected to an annulus, without using Khovanov homology. This provides two advantages: 1) the results hold for integer coefficients and 2) the spinc structures are more readily discernable. We apply this result to a branch locus which is a braid, and use the braid structure to find information about a fibered knot in the branched double cover. In some cases this provides all the information about the knot Floer homology and can be used to derive information about the Heegaard-Floer homology of associated fibered three manifolds. Results for certain positive braids are also included, establishing results similar to E. Eftekhary's in the Heegaard-Floer setting.