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math.GT2009★ 2 cited
Minimal Numbers of Fox Colors and Quandle Cocycle Invariants of Knots
Masahico Saito
Relations will be described between the quandle cocycle invariant and the minimal number of colors used for non-trivial Fox colorings of knots and links. In particular, a lower bou…
math.GT2009★ 1 cited
Frobenius Modules and Essential Surface Cobordisms
J. Scott Carter, Masahico Saito
An algebraic system is proposed that represent surface cobordisms in thickened surfaces. Module and comodule structures over Frobenius algebras are used for representing essential…
math.GT2009
Symmetric Extensions of Dihedral Quandles and Triple Points of Non-orientable Surfaces
J. Scott Carter, Kanako Oshiro, Masahico Saito
Quandles with involutions that satisfy certain conditions, called good involutions, can be used to color non-orientable surface-knots. We use subgroups of signed permutation matric…