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

Mikael Vejdemo-Johansson

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

K-Theory and Homology 2010-05-14 v3 Algebraic Topology Representation Theory

Authors: Mikael Vejdemo-Johansson

Abstract

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.

Keywords

group cohomology a-infinity structure cyclic groups characteristic 2 higher operations cohomology algebra

Cite

@article{arxiv.0707.1637,
  title  = {A partial $A_\infty$-structure on the cohomology of $C_n\times C_m$},
  author = {Mikael Vejdemo-Johansson},
  journal= {arXiv preprint arXiv:0707.1637},
  year   = {2010}
}

Comments

11 pages, updated to official JHRS version.

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

Abstract

Keywords

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