2007/11/14 by Larry Smith · 1 voice · 1 citation
Mathematics · #History and Theory of Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematics and Applications #math.AT #msc:13A50 #msc:55S10
paper · pdf · doi:10.2140/gtm.2007.11.327
published as Geom. Topol. Monogr. 11 (2007) 327-348 · This is the version published by Geometry & Topology Monographs on 14 November 2007
openalex publication_date 2007/11/14 · arxiv created 2009/03/28 · arxiv published 2009/03/28 · arxiv updated 2009/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
The purpose of these notes is to provide an introduction to the Steenrod algebra in an algebraic manner avoiding any use of cohomology operations. The Steenrod algebra is presented as a subalgebra of the algebra of endomorphisms of a functor. The functor in question assigns to a vector space over a Galois field the algebra of polynomial functions on that vector space: the subalgebra of the endomorphisms of this functor that turns out to be the Steenrod algebra if the ground field is the prime field, is generated by the homogeneous components of a variant of the Frobenius map.