Resumen de A1-algebraic topology

Fabien Morel

• We present some recent results in A1-algebraic topology, which means both in A1-homotopy theory of schemes and its relationship with algebraic geometry. This refers to the classical relationship between homotopy theory and (differential) topology. We explain several examples of �motivic� versions of classical results: the theory of the Brouwer degree, the classification ofA1-coverings through theA1-fundamental group, the Hurewicz Theorem and the A1-homotopy of algebraic spheres, and the A1-homotopy classification of vector bundles.

  We also give some applications and perspectives.