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.
Bibliographical noteFunding Information:
The research of Blanc was supported by Israel Science Foundation grants 74/11 and 770/16, and that of Sen by INSPIRE grant No. IFA MA-12.
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- Cosimplicial resolution
- Higher cohomology operation
- Toda bracket
ASJC Scopus subject areas
- Geometry and Topology