Steenrod operations and the diagonal morphism
S. S. Podkorytov
TL;DR
This paper presents a method to compute Steenrod operations in cohomology directly from the diagonal morphism and cyclic group action, avoiding additional complex data.
Contribution
It introduces a novel construction for Steenrod operations using only the diagonal morphism and group action, simplifying previous approaches.
Findings
Provides an explicit construction for Steenrod operations
Eliminates need for Eilenberg-Zilber morphisms
Simplifies computation of cohomology operations
Abstract
We show how to find the Steenrod operations in H^*(X) (the coefficients in F_p) given the diagonal morphism d_#:S_*(X)->S_*(X^p) and the action of the cyclic group C_p on S_*(X^p). Our construction needs no other data such as Eilenberg-Zilber morphisms.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · History and Theory of Mathematics · Advanced Differential Geometry Research