After a brief review of quandle cocycle invariants of knots and
knotted surfaces, we will present results on the tangle embedding
problem we have obtained using cocycle invariants.
We use the table of tangles given by T. Kanenobu, H. Saito,
and S. Satoh, and examine how much information we obtain
from the quandle cocycle invariants, as to which tangles
can or can not be embedded in which knots in the knot table.
This is a group research project, and the members consist of
K. Ameur, M. Elhamdadi, T. Rose, C. Smudde, and the speaker.