This article is cited in 11 papers

Homotopy classification of elliptic operators on stratified manifolds

V. E. Nazaikinskii^a, A. Yu. Savin^b, B. Yu. Sternin<sup>c

a</sup> M. V. Lomonosov Moscow State University
^b Independent University of Moscow
^c Moscow Institute of Electronic Engineering

Abstract: We give a homotopy classification of elliptic operators on a stratified manifold. Namely, we establish an isomorphism between the set of elliptic operators modulo stable homotopy and the $K$-homology group of the manifold. By way of application, we obtain an explicit formula for the obstruction of Atiyah–Bott type to the existence of Fredholm problems in the case of stratified manifolds.

UDC: 515.168.5+517.986.32

MSC: Primary 46L80; Secondary 19K33, 58J40

Received: 06.02.2006

DOI: 10.4213/im781

 English version: Izvestiya: Mathematics, 2007, 71:6, 1167–1192

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