A1-algebraic topology

• Autores: Fabien Morel
• Localización: Proceedings oh the International Congress of Mathematicians: Madrid, August 22-30,2006 : invited lectures / coord. por Marta Sanz Solé , Javier Soria de Diego , Juan Luis Varona Malumbres , Joan Verdera , Vol. 2, 2006, ISBN 978-3-03719-022-7, págs. 1035-1060
• Idioma: inglés
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• Resumen

  • 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.