Geometry of Foliations

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This text describes work on the differential geometry of foliations, in particular Riemannian foliations, done in the last few years. Sections on the Hodge theory for the transversal Laplace operator, and on applications of the heat equation method to Riemannian foliations are of particular note. There are chapters on the spectral theory for Riemannian foliations, on the author’s point of view of foliations as examples of noncommutative spaces, and on infinite-dimensional examples of Riemannian foliations.