Motivic Hopf elements and relations

2013/07/24 by Daniel Dugger, Daniel C. Isaksen, Dugger, Daniel +1 · 1 citation
Mathematics · #14F42 #55Q45 #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:14F42 #msc:55Q45

paper · pdf · doi:10.48550/arxiv.1307.6596

openalex publication_date 2013/07/24 · arxiv created 2013/07/26 · arxiv updated 2013/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use Cayley-Dickson algebras to produce Hopf elements eta, nu and sigma in the motivic stable homotopy groups of spheres, and we prove via geometric arguments that the the products eta*nu and nu*sigma both vanish. Along the way we develop several basic facts about the motivic stable homotopy ring.

Citations

• Splitting vector bundles outside the stable range and A¹-homotopy sheaves of punctured affine spaces
• On the Algebras Formed by the Cayley-Dickson Process

Cited by

• Equivariant Framed 1-Manifolds and the Pontryagin-Thom Isomorphism

Related

• Motivic homotopy theory and stable homotopy groups
• The Structure of Motivic Homotopy Groups
• The second stable homotopy groups of motivic spheres
• Stable homotopy groups of spheres: From dimension 0 to 90
• Remarks on motivic Moore spectra