On Elliptic Differential Operators with Shifts II. The Cohomological Index Formula
نویسنده
چکیده
This paper is a continuation of [1], where we have studied a general class of (pseudo)differential operators with nonlocal coefficients, referred to as operators with shifts, and obtained a local index formula (i.e., a formula expressing the index as the integral of a differential form explicitly determined by the principal symbol of the operator) for matrix elliptic operators of this kind. In the present paper we finish the business by establishing a cohomological index formula of Atiyah–Singer type for elliptic differential operators with shifts acting between section spaces of arbitrary vector bundles. The key step is the construction of closed graded traces on certain differential algebras over the symbol algebra for this class of operators. We do not formally assume the reader to be familiar with [1] as far as definitions are concerned but freely use the results obtained there. We also do not reproduce the discussion of general motivations for this research, which, as well as the bibliography, can be found in [1].
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On Elliptic Differential Operators with Shifts
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