9 papers
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.…
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…
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,…