The Baum–Connes conjecture: an extended survey

  • Maria Paula Gomez Aparicio
  • Pierre Julg
  • Alain ValetteEmail author


We present a history of the Baum–Connes conjecture, the methods involved, the current status, and the mathematics it generated.



Thanks are due to J.-B. Bost, R. Coulon, N. Higson, V. Lafforgue, P.-Y. Le Gall, H. Oyono-Oyono, N. Ozawa, and M. de la Salle for useful conversations and exchanges.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Maria Paula Gomez Aparicio
    • 1
  • Pierre Julg
    • 2
  • Alain Valette
    • 3
    Email author
  1. 1.Laboratoire de Mathématiques d’OrsayUniv. Paris-Sud, CNRS, Université Paris-SaclayOrsayFrance
  2. 2.Institut Denis Poisson, Université d’OrléansCollegium Sciences et Techniques, Bâtiment de mathématiquesOrléansFrance
  3. 3.Institut de MathématiquesUniversité de NeuchâtelNeuchâtelSwitzerland

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