3 papers
math.GT2026
On computational complexity of Khovanov homology
Tuomas Kelomäki, Dirk Schütz
Computing the Jones polynomial of general link diagrams is known to be P-hard, while restricting the computation to braid closures on fixed number of strands allows for a polyn…
math.GT2025
Morse matchings and Khovanov homology of 4-strand torus links
Tuomas Kelomäki
Given a link or a tangle diagram, we define algorithmic Morse theoretic simplifications on their Khovanov homology. In contrast to Bar-Natan's scanning algorithm, the cancellations…
math.GT2024
Discrete Morse Theory for Khovanov Homology
Tuomas Kelomäki
The standard methods for calculating Khovanov homology rely either on long exact/spectral sequences or on the algorithmic "divide and conquer" approach developed by Bar-Natan. In t…