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Higher cohomology operations and $R$–completion

David Blanc and Debasis Sen

Algebraic & Geometric Topology 18 (2018) 247–312

Let R be either Fp 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 f0,f1: Z Y between R–good spaces (inducing the same algebraic homomorphism H(Y ;R) H(Z;R)) are R–equivalent.

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higher cohomology operation, Toda bracket, cosimplicial resolution
Mathematical Subject Classification 2010
Primary: 55P60
Secondary: 55N99, 55P15, 55P20
Received: 5 September 2016
Revised: 4 May 2017
Accepted: 22 May 2017
Published: 10 January 2018
David Blanc
Department of Mathematics
University of Haifa
Debasis Sen
Department of Mathematics and Statistics
Indian Institute of Technology, Kanpur