2006/07/10 by Lawrence P. Roberts, Lawrence Roberts · 2 citations
Mathematics · Medicine · #Algebra over a field #Amino acid #Anatomy #Botulinum Toxin and Related Neurological Disorders #Braid #Cellular homology #Combinatorics #Euler characteristic #Floer homology #Geometric and Algebraic Topology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Khovanov homology #Knot (papermaking) #Knot invariant #Knot polynomial #Knot theory #Mathematics #Morse homology #Pure mathematics #Relative homology #Symplectic geometry #Torsion (gastropod) #math.GT
paper · pdf · doi:10.2140/agt.2009.9.29
published in Algebraic & Geometric Topology 9(1), 29-101 (Mathematical Sciences Publishers) · 57 pages
arxiv created 2006/07/10 · openalex publication_date 2009/01/06 · arxiv updated 2014/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We extend knot Floer homology to string links in D 2 I and to d -based links in arbitrary three manifolds. As with knot Floer homology we obtain a description of the Euler characteristic of the resulting homology groups (in D 2 I ) in terms of the torsion of the string link. Additionally, a state summation approach is described using the equivalent of Kauffman states. Furthermore, we examine the situation for braids, prove that for alternating string links the Euler characteristic determines the homology, and develop similar composition formulas and long exact sequences as in knot Floer homology.