Exotic Hopf maps, weight shifting and applications to vector bundles

TL;DR

This paper uses motivic homotopy theory to explicitly construct polynomial representatives of the suspension of the Hopf map and derives a rank 2 vector bundle on a specific algebraic variety.

Contribution

It introduces explicit polynomial representatives of the suspended Hopf map and constructs a new rank 2 vector bundle over the Jouanolou device of projective 3-space.

Findings

Explicit polynomial representatives of the suspended Hopf map over integers.

Construction of a rank 2 vector bundle on the Jouanolou device of P^3.

Application of motivic homotopy theory to algebraic vector bundles.

Abstract

Using motivic homotopy theory we produce several explicit polynomial representatives of the suspension of the Hopf map defined over the integers. We derive from this computation an explicit rank 2 vector bundle on the Jouanolou device of the projective space of dimension 3 over the integers.