2007/03/01 by Dror Bar-Natan · 3 citations
Mathematics · Computer Science · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #Khovanov homology #Tangle #Mathematics #Computation #Pure mathematics #Algebra over a field #Algorithm
paper · doi:10.1142/s0218216507005294
openalex publication_date 2007/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We introduce a local algorithm for Khovanov homology computations — that is, we explain how it is possible to "cancel" terms in the Khovanov complex associated with a ("local") tangle, hence canceling the many associated "global" terms in one swoosh early on. This leads to a dramatic improvement in computational efficiency. Thus our program can rapidly compute certain Khovanov homology groups that otherwise would have taken centuries to evaluate.