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Baum–Connes Conjecture
In mathematics, specifically in operator K-theory, the Baum–Connes conjecture suggests a link between the operator K-theory, K-theory of the reduced C*-algebra of a group theory, 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. The conjecture, if true, would have some older famous conjectures as consequences. For instance, the surjectivity part implies the Kaplansky's conjectures#Group rings, Kadison–Kaplansky conjecture for discrete torsion-free groups, and the injectivity is closely related to the Novikov conjecture. The conjecture is also closely related to index theory, as the assembly map \mu is a sort of index, and it plays a major role in Alain Connes' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baum And Connes
Baum is a German surname meaning "tree" (not to be confused with the French language, French surname Baume (surname), Baume). Notable people with this surname include: * Andreas Baum (born 1978), German politician * Bernie Baum (1929–1993), American songwriter * Bruce Baum (born 1952), American comedian * Carl Edward Baum (1940–2010), American electrical engineer * Carol Baum, American film producer * Christina Baum (born 1956), German politician * Dale Baum, (born 1943), American historian and professor * Walter Emerson Baum#Family life, Edgar Schofield Baum (1916–2006), American artist, physician, and WW2 combat medical officer * Fran Baum, Australian social scientist * Frank Baum (footballer) (born 1956), German footballer * Frank Joslyn Baum (1883–1958), American lawyer, soldier, writer and film producer * Friedrich Baum (1727–1777), colonel in British service during the American revolutionary war * Gerhart Baum (1932–2025), German lawyer and politician, mini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |