arXiv subjects

Hajime Kubota

Publications and source records attributed to Hajime Kubota.

6 recordsLinked to original sources

arXiv2026

Combinatorial knot Floer homology and tangle decompositions

We partially determine grid homology (combinatorial knot Floer homology) of diagonal knots, which are conjectured to be equivalent to positive braid knots, by exploiting nice grid diagrams. Its next-to-top term detects the number of prime factors, and the $\text{top}-2$ term corresponds to the decompositions of the knot into two non-integer tangles. We compare diagonal knots to various classes of knots, such as positive braids, fibered positive knots, and $L$-space knots.

math.GT↗

arXiv2024

On the Upsilon invariant in grid homology

The Upsilon invariant is a concordance invariant in knot Floer homology. Földvári reconstructed the Upsilon invariant using grid homology. We prove that the Upsilon invariant in knot Floer homology and one in grid homology are equivalent. Furthermore, we show some properties of the Upsilon invariant in the framework of grid homology.

math.GT↗

arXiv2024

Quasi-isomorphism of grid chain complexes for a connected sum of knots

We give a purely combinatorial proof of a Künneth formula for the minus version of knot Floer homology of connected sums by constructing a quasi-isomorphism of grid chain complexes. The quasi-isomorphism naturally deduces that the Legendrian and transverse invariants behave functorially with respect to the connected sum operation.

math.GT↗

arXiv2024

Grid homology for spatial graphs and a Künneth formula of connected sum

In this paper, we research the grid homology for spatial graphs with cut edges. We show that the grid homology for spatial graph $f$ is trivial if $f$ has sinks, sources, or cut edges. As an application, we give purely combinatorial proofs of some formulas including a Künneth formula for the knot Floer homology of connected sums in the framework of the grid homology.

math.GT↗

arXiv2023

Concordance invariant $Υ$ for balanced spatial graphs using grid homology

The $Υ$ invariant is a concordance invariant defined by using knot Floer homology. Földvári gives a combinatorial restructure of it using grid homology. We extend the combinatorial $Υ$ invariant for balanced spatial graph using grid homology for balanced spatial graph. Regarding links as spatial graphs, we give a upper and lower bounds for $Υ$ when two links are connected by a cobordism. Also we show that the combinatorial $Υ$ is a concordance invariant for knots.

math.GT↗

arXiv2023

Some properties of grid homology for MOY graphs

Grid homology for MOY graphs is immediately defined from grid homology for transverse spatial graphs developed by Harvey and O'Donnol in 2017. We studied some properties of grid homology for MOY graphs such as the oriented skein relation, the effect of contracting an edge, and the effect of uniting parallel edges with the same orientation.

math.GT↗