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

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

2008-01-19

arxiv.org/abs/0801.3010v2

Mathematics

Algebraic Topology

This duplicate posting of the paper has been withdrawn in favour of the posting at arXiv:0707.1637.

Scientific paper

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.

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