Couplings of $3$-anchored Bundles

Begüm Ateşli; Oğul Esen; Serkan Sütlü

Couplings of $3$-anchored Bundles

Differential Geometry 2026-07-02 v1

Authors: Begüm Ateşli , Oğul Esen , Serkan Sütlü

Abstract

This work develops an algebraic framework for merging two $3$ -anchored bundles over the same base manifold, equipped with mutual actions and two twisted cocycle terms, so as to obtain a $3$ -Lie algebroid structure on the corresponding Whitney sum. We also record the purely algebraic counterpart of this construction, namely the bicocycle double cross product $3$ -Lie algebra, obtained by removing the anchor and Leibniz-type compatibility conditions. The resulting framework provides a unified setting for $3$ -Lie algebroids and contains, as special cases, unified products, double cross products, semi-direct products, cocycle extensions, and direct products.

Keywords

3-anchored bundles 3-Lie algebroids Whitney sum twisted cocycle bicocycle double cross product 3-Lie algebra

Cite

@article{arxiv.2607.02397,
  title  = {Couplings of $3$-anchored Bundles},
  author = {Begüm Ateşli and Oğul Esen and Serkan Sütlü},
  journal= {arXiv preprint arXiv:2607.02397},
  year   = {2026}
}