• JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
 
  Bookmark and Share
 
 
Thèse de Doctorat
DOI
https://doi.org/10.11606/T.45.2020.tde-27042020-232832
Document
Auteur
Nom complet
Fernando Studzinski Carvalho
Adresse Mail
Unité de l'USP
Domain de Connaissance
Date de Soutenance
Editeur
São Paulo, 2019
Directeur
Jury
Gonzalez, Cristian Andres Ortiz (Président)
Brahic, Olivier
Hoyo, Matias Luis del
Jardim, Marcos Benevenuto
Struchiner, Ivan
Titre en anglais
On the cohomology of representations up to homotopy of Lie groupoids
Mots-clés en anglais
Cohomology
Lie groupoid
Representation up to homotopy
Simplicial manifold
Resumé en anglais
We study the concept of representations up to homotopy of Lie groupoids. Our main result is the proof that the cohomology of a Lie groupoid with coefficients in a representation up to homotopy is a Morita invariant of the groupoid. This can be interpreted as a way to provide cohomological invariants for orbifolds and more generally for differentiable stacks, which are spaces with singularities whose isomorphism classes are in one-to-one correspondence with Morita equivalence classes of Lie groupoids. To prove this result, we rely on the theory of simplicial objects in smooth categories e.g. simplicial manifolds, sim- plicial vector bundles, and equivalences between them which are defined in terms of maps called hypercovers. We also prove results on the invariance of the simplicial cohomology of these spaces under hypercovers.
Titre en portugais
Sobre a cohomologia de representações a menos de homotopia de grupoides de Lie
Mots-clés en portugais
Cohomology
Lie groupoid
Representation up to homotopy
Simplicial manifold
Resumé en portugais
Estudamos o conceito de representações a menos de homotopia de grupoides de Lie e a cohomologia naturalmente associada a tais representações. Nosso principal resultado é a prova de que a cohomologia de um grupoide de Lie com valores em uma representação a menos de homotopia é um invariante de Morita, o que pode ser interpretado como uma forma de introduzir invariantes cohomologicos para orbifolds e mais geralmente para stacks diferenciáveis, que são espaços com singularidades cujas classes de isomorfismo estão em correspondência biunvoca com classes de equivalência de Morita de grupoides de Lie. Para provar tal resultado, utilizamos a teoria de objetos simpliciais em categorias suaves e.g. variedades simpliciais, fibrados vetoriais simpliciais e equivalências entre eles, definidas a partir de mapas chamados hypercovers. Demonstramos também a invariância da cohomologia simplicial destes objetos sob hypercovers.
 
AVERTISSEMENT - Regarde ce document est soumise à votre acceptation des conditions d'utilisation suivantes:
Ce document est uniquement à des fins privées pour la recherche et l'enseignement. Reproduction à des fins commerciales est interdite. Cette droits couvrent l'ensemble des données sur ce document ainsi que son contenu. Toute utilisation ou de copie de ce document, en totalité ou en partie, doit inclure le nom de l'auteur.
ThesisFerStudzinski.pdf (874.15 Kbytes)
Date de Publication
2020-04-28
 
AVERTISSEMENT: Apprenez ce que sont des œvres dérivées cliquant ici.
Tous droits de la thèse/dissertation appartiennent aux auteurs
CeTI-SC/STI
Bibliothèque Numérique de Thèses et Mémoires de l'USP. Copyright © 2001-2021. Tous droits réservés.