arXiv subjects
Publications and source records attributed to Stella Shah.
We introduce a new family of invariants of oriented classical and virtual knots and links using fares, maps from paths in biquandle-colored diagrams to an abelian coefficient group. We consider the cases of 1-fares and 2-fares, provide examples to show that the enhancements are proper and end with some open questions about the cases of n-fares for n > 2.
The forbidden moves in virtual knot theory can be used to unknot any knot, virtual or classical; however, multi-component crossings in links can still survive, resulting a fused link. Using the forbidden moves, we categorify fused links obtain a quiver-valued invariant of classical and virtual links we call the forbidden quiver, opening the way for functors to and from other categories. As an application we use the forbidden quiver to obtain three polynomial invariants of virtual and classical links. Since these invariants are not sensitive to single-component crossing change, they are also link homotopy invariants.