2018/10/31 by Akram Alishahi, Alishahi, Akram, Nathan Dowlin +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Biochemical and Structural Characterization #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1810.13406
openalex publication_date 2018/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we introduce a chain complex C1 ± 1(D) where D is a plat braid diagram for a knot K. This complex is inspired by knot Floer homology, but it the construction is purely algebraic. It is constructed as an oriented cube of resolutions with differential d=d0+d1. We show that the E2 page of the associated spectral sequence is isomorphic to the Khovanov homology of K, and that the total homology is a link invariant which we conjecture is isomorphic to δ-graded knot Floer homology. The complex can be refined to a tangle invariant for braids on 2n strands, where the associated invariant is a bimodule over an algebra An. We show that An is isomorphic to B'(2n+1, n), the algebra used for the DA-bimodule constructed by Ozsvath and Szabo in their algebraic construction of knot Floer homology.