Secondary cohomology operations and the loop space cohomology

2024/09/07 by Samson Saneblidze, Saneblidze, Samson
Mathematics · #Commutative Algebra and Its Applications #Homotopy and Cohomology in Algebraic Topology #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.2409.04861

Abstract

Motivated by the loop space cohomology we construct the secondary operations on the cohomology H^*(X; ℤ_p) to be a Hopf algebra for a simply connected space X. The loop space cohomology ring H^*(ΩX; ℤ_p) is calculated in terms of generators and relations. This answers to A. Borel's decomposition of a Hopf algebra into a tensor product of the monogenic ones in which the heights of generators are determined by means of the action of the primary and secondary cohomology operations on H^*(X;ℤ_p). An application for calculating of the loop space cohomology of the exceptional group F₄ is given.

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