A partial $A_infty$-structure on the cohomology of $C_ntimes C_m$

Suppose k is a field of characteristic 2, and $n,m\geq 4$ powers of 2. Then the $A_\infty$-structure of the group cohomology algebras $H^(C_n,k)$ and $(H^(C_m,k)$ are well known. We give results characterizing an $A_\infty$-structure on $H^*(C_n\times C_m,k)$ including limits on non-vanishing low-arity operations and an infinite family of non-vanishing higher operations.

💡 Research Summary

The paper investigates the A∞‑algebra structure on the cohomology ring H⁎(Cₙ×Cₘ; k) where k is a field of characteristic 2 and n, m ≥ 4 are powers of 2. The cohomology of a single cyclic group Cₙ is well understood: it is the exterior‑polynomial algebra Λ(x)⊗k