Automorphisms, cohomology and extensions of symmetric quandles
Abstract
It is well-known that the cohomology of symmetric quandles generates robust cocycle invariants for unoriented classical and surface links. Expanding on the recently introduced module-theoretic generalized cohomology for symmetric quandles, we derive a four-term exact sequence that relates 1-cocycles, second cohomology, and a specific group of automorphisms associated with the extensions of symmetric quandles. This exact sequence shows that the obstruction to lifting and extending automorphisms is found in the second symmetric quandle cohomology, which we also illustrate by examples. Additionally, some general aspects of dynamical cocycles and extensions are discussed.
Fields of Study & Subjects
Advanced Topics in Algebra
Advanced Differential Equations and Dynamical Systems
Advanced Algebra and Geometry
Publication details
- Journal / source
- Homology Homotopy and Applications
- Volume
- 28
- Issue
- 3
- Pages
- 31–50
- Publication date
- 1 January 2026
- Language
- EN