Knot invariants from XC-structures on the Sweedler algebra are trivial
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.
Fields of Study & Subjects
Geometric and Algebraic Topology
Advanced Topics in Algebra
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 27 January 2026
- Language
- EN
- Document type
- Preprint