66 citations · 232 across the 47 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…
A Theorem of Sanderson on Link Bordisms in Dimension 4
J. Scott Carter, Seiichi Kamada, Masahico Saito +1
The groups of link bordism can be identified with homotopy groups via the Pontryagin-Thom construction. B.J. Sanderson computed the bordism group of 3 component surface-links using…
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…