T. Ito

collaborators

7 papers

math.GT2026

A partial classification of 3-dimensional clasp number two, genus two fibered knots

Tetsuya Ito

The 3-dimensional clasp number $c l (K)$ of a knot $K$ is the minimum number of clasp singularities of clasp disk, a singular immersed disk bounding $K$ whose singular set consists o…

math.GT2025

Weak rectangular diagrams, multi-crossing number, and arc index

Tetsuya Ito

For a non-split multi-crossing diagram $D$ of a link $L$ we show that $I^\pm (L) - 2 \leq c_{2} (D) + \sum_{n > 2} (2 n - 4) c_{n} (D)$ holds. Here $I^\pm (L)$ is the arc index and $c_{n} (D)$ is the numbe…

math.GT2025

On the negative band number

Michele Capovilla-Searle, Tetsuya Ito, Keiko Kawamuro +1

We study the negative band number of braids, knots, and links using Birman, Ko, and Lee's left-canonical form of a braid. As applications, we characterize up to conjugacy strongly…

math.GT2025

A slice Cromwell inequality of homogeneous links

Tetsuya Ito

Cromwell proved that the minimum $v$ -degree of the HOMFLY polynomial of homogeneous link $L$ is bounded above by $1 - I ¨ (L)$ , where $I ¨ (L)$ is the maximum Euler characteristic of Sei…

math.GT2025

Errata: A note on orientation-reversing distance one surgeries on non-null-homologous knots

Tetsuya Ito

The author would like to report an error of [T. Ito, Proc. Amer. Math. Soc. 152 (2024), pp. 4515--4519.] (version 1 of the arXiv:2311.08676) )

math.GT2025

Satellite fully positive braid links are braided satellite of fully positive braid links

Tetsuya Ito

A link in $S^{3}$ is a fully positive braid link if it is the closure of a positive braid that contains at least one full-twist. We show that a fully positive braid link is a satel…