Loterre: Mathematics: Baum-Connes conjecture

topology > algebraic topology > K-theory > Baum-Connes conjecture

mathematical physics > string theory > K-theory > Baum-Connes conjecture

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Baum-Connes conjecture

In mathematics, specifically in operator K-theory, the Baum–Connes conjecture suggests a link between the K-theory of the reduced C*-algebra of a group and the K-homology of the classifying space of proper actions of that group. The conjecture sets up a correspondence between different areas of mathematics, with the K-homology of the classifying space being related to geometry, differential operator theory, and homotopy theory, while the K-theory of the group's reduced C*-algebra is a purely analytical object.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Baum%E2%80%93Connes_conjecture)

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