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Knot invariants from XC-structures on the Sweedler algebra are trivial
Jorge Becerra
An XC-algebra is the minimum algebraic structure needed to define a framed, oriented knot invariant and generalises Lawrence's invariant obtained from ribbon Hopf algebras. In this…
XC-tangles and universal invariants
Jorge Becerra
We introduce a class of decorated abstract graphs, that we call XC-tangles, that provides a very convenient framework to study quantum invariants of tangles and virtual tangles. Th…
Minimal generating sets of rotational Reidemeister moves
Jorge Becerra, Kevin van Helden
Rotational tangle diagrams have been proven to be extremely important in the study of quantum invariants, as they provide a natural passage between topology and quantum algebra. In…
A refined functorial universal tangle invariant
Jorge Becerra
The universal invariant with respect to a given ribbon Hopf algebra is a tangle invariant that dominates all the Reshetikhin-Turaev invariants built from the representation theory…
On Bar-Natan - van der Veen's perturbed Gaussians
Jorge Becerra
We elucidate further properties of the novel family of polynomial time knot polynomials devised by Bar-Natan and van der Veen based on the Gaussian calculus of generating series fo…