Geodesic
Index theory and non-commutative geometry on foliated manifolds
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 64 (2009) no. 2, pp. 273-391

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This paper gives a survey of the index theory of tangentially elliptic and transversally elliptic operators on foliated manifolds as well as of related notions and results in non-commutative geometry. 
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     author = {Yu. A. Kordyukov},
     title = {Index theory and non-commutative geometry on foliated manifolds},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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Yu. A. Kordyukov. Index theory and non-commutative geometry on foliated manifolds. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 64 (2009) no. 2, pp. 273-391. http://geodesic.mathdoc.fr/item/RM_2009_64_2_a2/