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A partial $A_\infty$-structure on the cohomology of $C_n \times C_m$
#
A partial $A_\infty$-structure on the cohomology of $C_n \times C_m$

##
Mikael Vejdemo-Johansson

Suppose $k$ is a finite field, and $n,m\geq 4$ multiples of the field
characteristic. 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.

Journal of Homotopy and Related Structures, Vol. 3(2008), No. 1, pp. 1-11