On a Conjecture of Mahowald on the Cohomology of Finite Sub-Hopf\n algebras of the Steenrod Algebra

2019/05/07 by Paul Shick, Shick, Paul
Mathematics · Social Sciences · #55Q51 #55T15 #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematics Education and Teaching Techniques #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1905.02625

openalex publication_date 2019/05/07 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

Mahowald's conjecture arose as part of a program attempting to view chromatic\nphenomena in stable homotopy theory through the lens of the classical Adams\nspectral sequence. The conjecture predicts the existence of nonzero classes in\nthe cohomology of the finite sub-Hopf algebras A(n) of the mod 2 Steenrod\nalgebra that correspond to generators in the homotopy rings of certain periodic\nspectra. The purpose of this note is to present a proof of the conjecture.\n

Related

• Extending Adams' theorem from singly generated to periodic cohomology
• The Mahowald operator in the cohomology of the Steenrod algebra
• The cohomology of motivic A(2)
• The motivic Adams spectral sequence
• Hopf algebras in the cohomology of A_g, GL_n(ℤ), and SL_n(ℤ)