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Noncommutative geometry associates a $C^*$-algebra $C^*(S,{\cal F})$ with a foliation $\cal F$ on a manifold $S.$

  1. Did somebody study this construction for noncompact surfaces $S$?
  2. What I am really interested in is an extension of the above construction to surface $S$ foliations admitting some singularities (like $k$-pronged singularities in Thurston's theory of measured surface foliations). Is there a version of $C^*(S,{\cal F})$ for such foliations more reasonable than that for $S$ with singularities of $\cal F$ removed?
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