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

Suppose $k$ is a field of characteristic 2, and $n,mgeq 4$ 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 $H^*(C_ntimes C_m,k)$ including limits on non-vanishing low-arity operations and an infinite family of non-vanishing higher operations.

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

Suppose k is a field of characteristic 2, and $n,mgeq 4$ 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 $H^*(C_ntimes C_m,k)$ including limits on non-vanishing low-arity operations and an infinite family of non-vanishing higher operations.

Blackbox computation of $A_infty$-algebras

Kadeishvilis proof of the minimality theorem induces an algorithm for the inductive computation of an $A_infty$-algebra structure on the homology of a dg-algebra. In this paper, we prove that for one class of dg-algebras, the resulting computation will generate a complete $A_infty$-algebra structure after a finite amount of computational work.

Enumerating the Saneblidze-Umble diagonal terms

The author presents a computer implementation, calculating the terms of the Saneblidze-Umble diagonals on the permutahedron and the associahedron. The code is analyzed for correctness and presented in the paper, the source code of which simultaneously represents both the paper and the program.