De rham cohomology in diffeological spaces

• Autores: Reihaneh Mehrabi
• Directores de la Tesis: Enrique Macías-Virgós (dir. tes.) , Antonio Gómez Tato (dir. tes.)
• Lectura: En la Universidade de Santiago de Compostela ( España ) en 2024
• Idioma: inglés
• Tribunal Calificador de la Tesis: Jesús Antonio Álvarez López (presid.) , Esperanza Sanmartín Carbón (secret.) , Akbar Dehghan Nezhad (voc.)
• Enlaces
  • Tesis en acceso abierto en: MINERVA
• Resumen

  • Diffeological spaces are a generalization of smooth manifolds. They were intro- duced around 1970 by the French mathematician and physicist Jean-Marie Souriau (1922-2012), in an attempt to formalize quantum mechanics and geometric quantiza- tion. This approach proved to be useful in several settings which involve objects that rarely are finite dimensional manifolds, like the space of smooth maps between two manifolds or the space of leaves of a foliation.

    In this thesis we are mainly interested in the Cartan calculus on diffeological spaces. We clarify the properties of the De Rham cohomology groups, which are typical of the algebraic topology of manifolds but were less known in this setting. We introduce several new constructions like the Mayer-Vietoris sequence, the relative De Rham cohomology groups and the relative cup-product.