11 papers
Homological lifts of Arnold invariants and
Noboru Ito
Viro's Euler-integral polynomial and the Lanzat--Polyak quantized-curvature polynomial refine Arnold's invariants and for generic immersed one-compone…
Commutators of pure twin groups and rondles
Noboru Ito
We formulate a relationship between finite-order rondle invariants with respect to triple-point modifications and the lower central series of subgroups of a pure twin group. Using…
Underlying Stokes and de Rham structures for Arnold-type invariants
Noboru Ito, Hiroki Mizuno
We introduce a framework on dual complexes for studying Arnold-type invariants of immersed curves and immersed surfaces via local finite-difference structures associated with Alexa…
An explicit slice formula for surface invariants via curve invariants
Noboru Ito, Hiroki Mizuno
We give an explicit slice formula for a surface invariant of generic immersions in , expressed in terms of curve invariants arising from planar slices. Using a motion…
Minimal Generating Sets of Singular Reidemeister Moves and Their Classification
Noboru Ito, Yuichiro Iwamoto
Singular knot theory extends classical knot theory by allowing transverse double points without over/under information, together with singular Reidemeister moves of types IV and V.…
B-type coefficient polynomial
Noboru Ito, Mayuko Kon
An A-type coefficient polynomial introduced by Kawauchi recovers the HOMFLY-PT polynomial as a formal power series within skein theory. A notable feature of this construction is th…
Genera of two-component alternating links
Noboru Ito, Nodoka Kawajiri
We extend the equality-type results of Ito--Takimura and Kindred for the non-orientable genera of alternating knots to the setting of two-component alternating links. We show that,…
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…
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…
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…
Lifting link invariants by functors on nanophrases
Tomonori Fukunaga, Noboru Ito
Nanophrases have a filtered structure consisting of an infinite number of categories, and each category has a homotopy structure. Among these categories, the one that we are most f…