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On the homotopy classification of elliptic operators on manifolds with corners. (English. Russian original) Zbl 1156.58011
Dokl. Math. 75, No. 2, 186-189 (2007); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 413, No. 1, 16-19 (2007).
From the introduction: This paper deals with elliptic theory on manifolds with corners. Such manifolds arise, e.g., as products of manifolds with boundary. We determine a natural dual object for a manifold with corners and show how a calculus of zeroth-order pseudodifferential operators (PDOs) on such a manifold can be constructed in terms of the localization principle on $$C^*$$-algebras. The definition uses induction on the “depth” of manifolds and has a natural formulation for operators with a parameter. The results are applied to solve Gelfand’s problem about a homotopy classification of elliptic operators for manifolds with corners. One of the consequences of the classification is an explicit formula for Atiyah-Bott-type obstructions to setting Fredholm problems.

##### MSC:
 58J40 Pseudodifferential and Fourier integral operators on manifolds 58J05 Elliptic equations on manifolds, general theory
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##### References:
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