The von Neumann algebra of a foliation

  • Alain Connes
Main Lectures
Part of the Lecture Notes in Physics book series (LNP, volume 80)


Every smooth foliation
of a manifold V gives rise very naturally to a von Neumann algebra
. The weights on M correspond exactly to operator valued forms on the “manifold” of leaves of
. We compute their modular automorphism group, this yields the continuous decomposition of M in terms of another foliation
of V and a one parameter group of automorphisms of
. We then illustrate this decomposition with a few examples.


Operator Density Compact Manifold Random Operator Ergodic Decomposition Transverse Bundle 
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© Springer-Verlag 1978

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  • Alain Connes

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