7 citations · 7 across the 2 of their papers we have counts for
5 papers · 2 filters
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…
Geometric Interpretations of Quandle Homology
J. Scott Carter, Seiichi Kamada, Masahico Saito
Geometric representations of cycles in quandle homology theory are given in terms of colored knot diagrams. Abstract knot diagrams are generalized to diagrams with exceptional poin…
Shifting Homomorphisms in Quandle Cohomology and Skeins of Cocycle Knot Invariants
J. Scott Carter, Daniel Jelsovsky, Seiichi Kamada +1
Homomorphisms on quandle cohomology groups that raise the dimensions by one are studied in relation to the cocycle state-sum invariants of knots and knotted surfaces. Skein relatio…