3 papers
math.GT2000
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…
math.GT1999
Quandle Homology Groups, Their Betti Numbers, and Virtual Knots
J. Scott Carter, Daniel Jelsovsky, Seiichi Kamada +1
Lower bounds of betti numbers for homology groups of racks and quandles will be given using the quotient homomorphism to the orbit quandles. Exact sequences relating various types…
math.GT1999
Quandle Cohomology and State-sum Invariants of Knotted Curves and Surfaces
J. Scott Carter, Daniel Jelsovsky, Seiichi Kamada +2
The 2-twist spun trefoil is an example of a sphere that is knotted in 4-dimensional space. Here this example is shown to be distinct from the same sphere with the reversed orientat…