Index of elliptic operators for a diffeomorphism

Abstract

We develop elliptic theory of operators associated with a diffeomorphism of a closed smooth manifold. The aim of the present paper is to obtain an index formula for such operators in terms of topological invariants of the manifold and of the symbol of the operator. The symbol in this situation is an element of a certain crossed product. We express the index as the pairing of the class in K-theory defined by the symbol and the Todd class in periodic cyclic cohomology of the crossed product.

37 pages

References in corpus (5)

• Type III and spectral triples
• Characters of Cycles, Equivariant Characteristic Classes and Fredholm Modules
• Local index formula and twisted spectral triples
• Elliptic operators in even subspaces
• The homotopy classification and the index of boundary value problems for general elliptic operators

Cited by in corpus (8)

• Analytic and algebraic indices of elliptic operators associated with discrete groups of quantized canonical transformations
• Elliptic theory for operators associated with diffeomorphisms of smooth manifolds
• Elliptic Operators Associated with Groups of Quantized Canonical Transformations
• Elliptic $G$-operators on manifolds with isolated singularities
• On the Index Formula for an Isometric Diffeomorphism
• Equivariant cyclic cocycles on the Boutet de Monvel symbol algebra
• Operator Algebras Associated with Quantized Canonical Transformations
• Index of nonlocal elliptic boundary value problems associated with isometric group actions