Knot invariants from XC-structures on the Sweedler algebra are trivial
Geometric Topology
2026-01-28 v1 Quantum Algebra
Abstract
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 note, we show that the knot invariant produced by any XC-structure on the Sweedler algebra is completely determined by the framing of the knot. Furthermore, we also exhibit explicit families of XC-structures on the Sweedler algebra that do not have a ribbon Hopf-algebraic origin.
Cite
@article{arxiv.2601.19840,
title = {Knot invariants from XC-structures on the Sweedler algebra are trivial},
author = {Jorge Becerra},
journal= {arXiv preprint arXiv:2601.19840},
year = {2026}
}
Comments
12 pages, comments are welcome