# Connes

### Some articles on connes:

Baum–Connes Conjecture
... In mathematics, specifically in operator K-theory, the Baum–Connes conjecture suggests a link between the K-theory of the C*-algebra of a group and the K-homology of the corresponding classifying space of ... related to index theory, as the assembly map is a sort of index, and it plays a major role in Alain Connes' noncommutative geometry program ...
Attempts To Prove The Riemann Hypothesis - Operator Theory
... In a connection with this quantum mechanical problem Berry and Connes had proposed that the inverse of the potential of the Hamiltonian is connected to the half-derivative of the function then, in Berry–Connes ... determinant (Hadamard product) as proven by Connes and others, in this approach ...
Subfactor - Principal Graphs
... The relative tensor product, described in Jones (1983) and often called Connes fusion after a prior definition for general von Neumann algebras of Alain Connes, can be used to define new ... It is multiplicative with respect to Connes fusion ...
Criticism Of Non-standard Analysis - Connes' Criticism
... Geometry and Physics 23 ('97), 206–234, Alain Connes wrote "The answer given by non-standard analysis, namely a nonstandard real, is equally disappointing every non-standard ... In his '95 article "Noncommutative geometry and reality" Connes develops a calculus of infinitesimals based on operators in Hilbert space ... Connes points out the following three aspects of Robinson's hyperreals Katz Katz analyze Connes' criticisms of non-standard analysis, and challenge the specific claims (1) and ...
Von Neumann Algebra - Factors - Type III Factors
... More precisely, if the Connes spectrum (of its modular group) is 1 then the factor is of type III0, if the Connes spectrum is all integral powers of λ for 0 < λ < 1, then the type is III ... The Connes spectrum is a closed subgroup of the positive reals, so these are the only possibilities.) The only trace on type III factors takes value ∞ on all non-zero positive ...