Displaying similar documents to “Homological index formulas for elliptic operators over C*-algebras.”

Characteristic classes for A -bundles

Cap, Andreas, Schichl, Hermann

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The authors generalize a construction of Connes by defining for an A -bundle E over smooth manifold X and a reduced cyclic cohomology class c a sequence of de Rham cohomology classes c h c k ( E ) . Here A is a convenient algebra, defined by the authors, and E is a locally trivial bundle with standard fibre a right finitely generated projective A -module and bounded A -modules homomorphisms as transition functions.

On the index of nonlocal elliptic operators for compact Lie groups

Anton Savin (2011)

Open Mathematics

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We consider a class of nonlocal operators associated with a compact Lie group G acting on a smooth manifold. A notion of symbol of such operators is introduced and an index formula for elliptic elements is obtained. The symbol in this situation is an element of a noncommutative algebra (crossed product by G) and to obtain an index formula, we define the Chern character for this algebra in the framework of noncommutative geometry.

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.

Holonomy, twisting cochains and characteristic classes

G. Sharygin (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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This paper contains a description of various geometric constructions associated with fibre bundles, given in terms of important algebraic object, the “twisting cochain". Our examples include the Chern-Weil classes, the holonomy representation and the so-called cyclic Chern character of Bismut and others (see [2, 11, 27]), also called the Bismut’s class. The later example is the principal one for us, since we are motivated by the attempt to find an algebraic approach to the Witten’s index...