2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/179807Higher nilpotent analogues of the $A-\infty$-structure are explicitly defined on arbitrary simplicial complexes, generalizing explicit construction of /hep-th/0704.2609. These structures are associated with the higher nilpotent differential $d_n$, satisfying $d_n^n =0$, which is naturally defined on triangulated manifolds (tetrahedral lattices). The deformation $D_n = (I + ε_n) d_n (I + ε_n)^{-1}$ is defined with the help of the $n$-versions of discrete exterior product $\wedge_n$ and the $K_n$-operator.preliminary version, essential corrections madeHigh Energy Physics - TheoryGeometric Topologytext