Extend the ribbon mechanism to higher dimensions

Determine whether a mechanism analogous to the two-dimensional ribbon structure exists in three and four dimensions, potentially using higher-gauge-theoretic data, in order to establish whether the semi-dual discretization is specific to two dimensions or reflects a more general construction.

Background

The ribbon construction simultaneously retains data associated with the triangulation and its dual complex, which is essential for the two-dimensional BF-to-Regge correspondence. In higher dimensions, an analogous structure may require more elaborate combinatorics or higher gauge theory.

The authors explicitly identify the existence and nature of such a higher-dimensional mechanism as unresolved, and its resolution would clarify whether the semi-dual structure found here is exceptional or part of a broader pattern.

References

An important question is whether an analogous mechanism exists in three and four dimensions. The higher-dimensional generalization may require a more elaborate combinatorial structure, possibly involving higher-gauge-theoretic data rather than an ordinary ribbon description. Understanding this extension would clarify whether the semi-dual discretization uncovered here is a peculiarity of two dimensions or the lower-dimensional manifestation of a more general mechanism.

— Regge Dilaton Gravity from BF Theory  (2610.21058 - Girelli et al., 15 Oct 2026) in Conclusion