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On the index of differential operators on manifolds with edges. (English. Russian original) Zbl 1125.58303
Dokl. Math. 69, No. 1, 68-71 (2004); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 394, No. 3, 309-312 (2004).
From the introduction: The aim of this paper is to construct index formulas for elliptic operators on manifolds with edges. It is well known that the ellipticity condition for such operators splits into two conditions, one of which pertains to the interior principal symbol defined on the smooth part of the manifold, and the other, to the edge symbol, which is an operator family on the cotangent space of the edge. Accordingly, our formulas comprise two terms, one of which is determined by the interior principal symbol, and the other, by the edge symbol. They are valid under some symmetry conditions imposed on the principal symbol on the edge. Furthermore, both terms are homotopy invariant in the respective classes.
58J22 Exotic index theories on manifolds
35J30 Higher-order elliptic equations