Titlebook: Elliptic Theory and Noncommutative Geometry; Nonlocal Elliptic Op Vladimir E. Nazaikinskii,Anton Yu. Savin,Boris Yu. Book 2008 Birkhäuser B

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Homotopy Classification operators on closed manifolds considered by Atiyah and Singer, the study of this problem naturally starts from establishing the homotopy classification of elliptic operators. It is well known that in the classical case this classification is given by the .-group with compact supports of the cotange

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Chern Characterngent bundle of the manifold . and the Chern character of the symbol. (Both are collections of cohomology classes defined on cotangent bundles of fixed-point manifolds . of the action of Г.) In this chapter, we describe the Chern character.

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Cohomological Index FormulaTd(. ⊗ ℂ; Г) of the complexified tangent bundle of the manifold . with a Г-action. Let us construct this class. It belongs to the product . of even degree cohomology groups of the fixed point submanifolds ., where .0 runs over representatives of all conjugacy classes in Г. (Recall that the fixed poi

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Index of Nonlocal Operators over ,*-Algebrasy [57], where one considers the index of local elliptic operators over .*-algebras and whose ideology we follow to a large extent here, the main role in the structure and the proof of such index formulas is played by the Künneth formula describing the .-group of tensor products of .*-algebras. To en

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Index Formula for a Finite Group Гonlocal equation . can be reduced to a system of local equations. To this end, we replace the functions . and . by the vector functions . whose components . are obtained as shifts of the original functions by the elements of Г.

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Book 2008tement (or at least admit an equivalent classical statement) but can be solved only in the framework of noncommutative geometry. One of such problems is the subject of the present book. The classical elliptic theory developed in the well-known work of Atiyah and Singer on the index problem relates a