New York Journal of Mathematics
Volume 19 (2013) 823-871


Daniel Dugger and Daniel C. Isaksen

Motivic Hopf elements and relations

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Published: November 21, 2013
Keywords: Motivic stable homotopy group, Hopf map
Subject: 14F42, 55Q45

We use Cayley-Dickson algebras to produce Hopf elements η, ν, and σ in the motivic stable homotopy groups of spheres, and we prove the relations ην=0 and νσ=0 by geometric arguments. Along the way we develop several basic facts about the motivic stable homotopy ring.


The first author was supported by NSF grant DMS-0905888. The second author was supported by NSF grant DMS-1202213.

Author information

Daniel Dugger:
Department of Mathematics, University of Oregon, Eugene, OR 97403

Daniel C. Isaksen:
Department of Mathematics, Wayne State University, Detroit, MI 48202