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math.GT2025
Minimal Generating sets of Reidemeister moves
Noboru Ito, Yuichiro Iwamoto
We determine whether each known generating set of arbitrary oriented Reidemeister moves is minimal. We then provide a complete classification of minimal generating sets that includ…
math.QA2025
Remark on twists of Frobenius algebra and link homology
Noboru Ito, Keita Nakagane, Jun Yoshida
We discuss twists on Frobenius algebras in the context of link homology. In his paper in 2006, Khovanov asserted that a twist of a Frobenius algebra yields an isomorphic chain comp…
math.GT2025
Arnold Strangeness of surface immersions
Noboru Ito, Hiroki Mizuno
It is known that for any smooth sphere eversion, the number of quadruple point jumps is always odd. In this paper, we define an integer-valued function that detects and classifies…