66 citations · 232 across the 47 of their papers we have counts for
5 papers · 2 filters
Quandle Homology Theory and Cocycle Knot Invariants
J. Scott Carter, Masahico Saito
This paper is a survey of several papers in quandle homology theory and cocycle knot invariants that have been published recently. Here we describe cocycle knot invariants that are…
Twisted quandle homology theory and cocycle knot invariants
J. Scott Carter, Mohamed Elhamdadi, Masahico Saito
The quandle homology theory is generalized to the case when the coefficient groups admit the structure of Alexander quandles, by including an action of the infinite cyclic group in…
Extensions of Quandles and Cocycle Knot Invariants
J. Scott Carter, Mohamed Elhamdadi, Marina Appiou Nikiforou +1
Quandle cocycles are constructed from extensions of quandles. The theory is parallel to that of group cohomology and group extensions. An interpretation of quandle cocycle invarian…
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…