Higher cohomology operations and R–completion

Blanc, David; Sen, Debasis

doi:10.2140/agt.2018.18.247

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Higher cohomology operations and $R$–completion

David Blanc and Debasis Sen

Algebraic & Geometric Topology 18 (2018) 247–312

DOI: 10.2140/agt.2018.18.247

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 $f_{0}, f_{1} : Z \to Y$ between $R$ –good spaces (inducing the same algebraic homomorphism $H^{*} (Y; R) \to H^{*} (Z; R)$ ) are $R$ –equivalent.

Keywords

higher cohomology operation, Toda bracket, cosimplicial resolution

Mathematical Subject Classification 2010

Primary: 55P60

Secondary: 55N99, 55P15, 55P20

References

Publication

Received: 5 September 2016

Revised: 4 May 2017

Accepted: 22 May 2017

Published: 10 January 2018

Authors

David Blanc
Department of Mathematics University of Haifa Haifa Israel

Debasis Sen
Department of Mathematics and Statistics Indian Institute of Technology, Kanpur Kanpur India

Volume 18, issue 1 (2018)