#### Volume 18, issue 1 (2018)

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Higher cohomology operations and $R$–completion

### David Blanc and Debasis Sen

Algebraic & Geometric Topology 18 (2018) 247–312
##### Abstract

Let $R$ be either ${\mathbb{F}}_{\phantom{\rule{0.3em}{0ex}}p}$ or a field of characteristic $0$. For each $R$–good topological space  $Y\phantom{\rule{0.3em}{0ex}}$, we define a collection of higher cohomology operations which, together with the cohomology algebra ${H}^{\ast }\left(Y;R\right)$, suffice to determine $Y$ up to $R$–completion. We also provide a similar collection of higher cohomology operations which determine when two maps ${f}_{0},{f}_{1}:Z\to Y$ between $R$–good spaces (inducing the same algebraic homomorphism ${H}^{\ast }\left(Y;R\right)\to {H}^{\ast }\left(Z;R\right)$) are $R$–equivalent.

##### Keywords
higher cohomology operation, Toda bracket, cosimplicial resolution
##### Mathematical Subject Classification 2010
Primary: 55P60
Secondary: 55N99, 55P15, 55P20