## Algebraic & Geometric Topology

### Higher cohomology operations and $R$–completion

#### Abstract

Let $R$ be either $F p$ or a field of characteristic $0$. For each $R$–good topological space  $Y$, we define a collection of higher cohomology operations which, together with the cohomology algebra $H ∗ ( Y ; R )$, suffice to determine $Y$ up to $R$–completion. We also provide a similar collection of higher cohomology operations which determine when two maps $f 0 , f 1 : Z → Y$ between $R$–good spaces (inducing the same algebraic homomorphism $H ∗ ( Y ; R ) → H ∗ ( Z ; R )$) are $R$–equivalent.

#### Article information

Source
Algebr. Geom. Topol., Volume 18, Number 1 (2018), 247-312.

Dates
Revised: 4 May 2017
Accepted: 22 May 2017
First available in Project Euclid: 1 February 2018

https://projecteuclid.org/euclid.agt/1517454217

Digital Object Identifier
doi:10.2140/agt.2018.18.247

Mathematical Reviews number (MathSciNet)
MR3748244

Zentralblatt MATH identifier
06828005

#### Citation

Blanc, David; Sen, Debasis. Higher cohomology operations and $R$–completion. Algebr. Geom. Topol. 18 (2018), no. 1, 247--312. doi:10.2140/agt.2018.18.247. https://projecteuclid.org/euclid.agt/1517454217

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