11 papers · 1 filter
Knot invariants derived from quandles and racks
Seiichi Kamada
The homology and cohomology of quandles and racks are used in knot theory: given a finite quandle and a cocycle, we can construct a knot invariant. This is a quick introductory sur…
Bordism of Unoriented Surfaces in 4-Space
J. Scott Carter, Seiichi Kamada, Masahico Saito +1
The group of bordism classes of unoriented surfaces in 4-space is determined. The bordism classes are characterized by normal Euler numbers,double linking numbers, and triple linki…
Diagrammatic Computations for Quandles and Cocycle Knot Invariants
J. Scott Carter, Seiichi Kamada, Masahico Saito
The state-sum invariants for knots and knotted surfaces defined from quandle cocycles are described using the Kronecker product between cycles represented by colored knot diagrams…
Stable Equivalence of Knots on Surfaces and Virtual Knot Cobordisms
J. Scott Carter, Seiichi Kamada, Masahico Saito
We introduce an equivalence relation, called stable equivalence, on knot diagrams and closed curves on surfaces. We give bijections between the set of abstract knots, the set of vi…
Braid presentation of virtual knots and welded knots
Seiichi Kamada
The notion of a virtual knot introduced by L. Kauffman induces the notion of a virtual braid. It is closely related with a welded braid of R. Fenn, R. Rimanyi and C. Rourke. Alexan…
Triple Linking of Surfaces in 4-Space
J. Scott Carter, Seiichi Kamada, Masahico Saito +1
Triple linking numbers were defined for 3-component oriented surface-links in 4-space using signed triple points on projections in 3-space. In this paper we give an algebraic formu…