Recursive Morse matchings compute integral Khovanov homology for all 4-strand torus links with at least 28 strands, including abundant 4-torsion and agreement with the Gorsky-Oblomkov-Rasmussen conjecture at infinity.
A spanning tree model for Khovanov homology, Rasmussen's s-invariant and exotic discs in the $4$-ball
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
The checkerboard coloring of knot diagrams offers a graph-theoretical approach to address topological questions. Champanerkar and Kofman defined a complex generated by the spanning trees of a graph obtained from the checkerboard coloring whose homology is the reduced Khovanov homology. Notably, the differential in their chain complex was not explicitly defined. We explicitly define the combinatorial form of the differential within the spanning tree complex. We additionally provide a description of Rasmussen's $s$-invariant within the context of the spanning tree complex. Applying our techniques, we identify a new infinite family of knots where each of them bounds a set of exotic discs within the 4-ball.
fields
math.GT 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Morse matchings and Khovanov homology of 4-strand torus links
Recursive Morse matchings compute integral Khovanov homology for all 4-strand torus links with at least 28 strands, including abundant 4-torsion and agreement with the Gorsky-Oblomkov-Rasmussen conjecture at infinity.