Displaying similar documents to “On the index of nonlocal elliptic operators for compact Lie groups”

On a class of nonlocal elliptic operators for compact Lie groups. Uniformization and finiteness theorem

Boris Sternin (2011)

Open Mathematics

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We consider a class of nonlocal operators associated with an action of a compact Lie group G on a smooth closed manifold. Ellipticity condition and Fredholm property for elliptic operators are obtained. This class of operators is studied using pseudodifferential uniformization, which reduces the problem to a pseudodifferential operator acting in sections of infinite-dimensional bundles.

Elliptic operators and higher signatures

Eric Leichtnam, Paolo Piazza (2004)

Annales de l’institut Fourier

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Building on the theory of elliptic operators, we give a unified treatment of the following topics: - the problem of homotopy invariance of Novikov’s higher signatures on closed manifolds, - the problem of cut-and-paste invariance of Novikov’s higher signatures on closed manifolds, - the problem of defining higher signatures on manifolds with boundary and proving their homotopy invariance.