Smooth torus actions are described by a single vector field

• Francisco Javier Turiel ^[1] ; Antonio Viruel ^[1]
  1. [1] Universidad de Málaga

     Universidad de Málaga

     Málaga, España

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 34, Nº 2, 2018, págs. 839-852
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Consider a smooth effective action of a torus Tn on a connected C∞-manifold M. Assume that M is not a torus endowed with the natural action. Then we prove that there exists a complete vector field X on M such that the automorphism group of X equals Tn×R, where the factor R comes from the flow of X and Tn is regarded as a subgroup of Diff(M). Thus one may reconstruct the whole action of Tn from a single vector field.