The differential \rm d₄(h₆³) in the Adams spectral sequence for spheres

2013/06/29 by Pomin Wu, Wu, Pomin
Engineering · Mathematics · #55Q45 #55T15 #Advanced Differential Equations and Dynamical Systems #Advanced Numerical Analysis Techniques #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.AT #msc:55Q45 #msc:55T15

paper · pdf · doi:10.48550/arxiv.1307.0064

arxiv created 2013/06/29 · openalex publication_date 2013/06/29 · arxiv updated 2013/07/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We show that there is a non-trivial differential d₄(h₆³) =h₀³g₄ in the mod 2 Adams spectral sequence for spheres. This together with the results in \citebarratt_differentials₁970,lin_differential₁998,kan_differential₂001 completely settle the differentials of h_i³ for i≥4. (The differentials of h_i³ for i=0,1,2,3 are well-known.) Our proof uses the Kevaire invariant elements θ_i ∈π_2ⁱ⁺¹-2^S for i=4,5 with the properties 2θ₄ =0, 2θ₅ =0.

Citations

• Genetics of Homotopy Theory and the Adams Conjecture

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