Higher cohomology operations and R-completion

David Blanc; Debasis Sen

doi:10.2140/agt.2018.18.247

Higher cohomology operations and R-completion

David Blanc, Debasis Sen

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 f₀,f₁: Z→Y between R-good spaces (inducing the same algebraic homomorphism H * (Y;R)→H * (Z;R)) are R-equivalent.

Original language	English
Pages (from-to)	247-312
Number of pages	66
Journal	Algebraic and Geometric Topology
Volume	18
Issue number	1
DOIs	https://doi.org/10.2140/agt.2018.18.247
State	Published - 10 Jan 2018

Bibliographical note

Funding 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.

Publisher Copyright:
© 2018, Mathematical Sciences Publishers. All rights reserved.

Keywords

Cosimplicial resolution
Higher cohomology operation
Toda bracket

ASJC Scopus subject areas

Geometry and Topology

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10.2140/agt.2018.18.247

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N2 - 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.

AB - 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 operations and R-completion

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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