Motivic Hopf elements and relations

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.

References in corpus (2)

• Motivic Brown-Peterson invariants of the rationals
• Splitting vector bundles outside the stable range and A^1-homotopy sheaves of punctured affine spaces

Cited by in corpus (6)

• The motivic Mahowald invariant
• The motivic Adams-Novikov spectral sequence at odd primes over $\mathbb{C}$ and $\mathbb{R}$
• R-motivic stable stems
• The $C_2$-effective spectral sequence for $C_2$-equivariant connective real $K$-theory
• Stable motivic pi_1 of low-dimensional fields
• The second stable homotopy groups of motivic spheres