Article

# On the Homotopy Classification of Elliptic Operators on Manifolds with Edges

04/2005;
Source: arXiv

ABSTRACT We obtain a classification of elliptic operators modulo stable homotopy on manifolds with edges (this is in some sense the simplest class of manifolds with nonisolated singularities). We show that the operators are classified by the K-homology group of the manifold. To this end, we construct exact sequence in elliptic theory isomorphic to the K-homology exact sequence. The main part of the proof is the computation of the boundary map using semiclassical quantization.

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15 Apr 2013

### Keywords

boundary map

elliptic operators modulo stable homotopy

elliptic theory isomorphic

K-homology exact sequence

K-homology group

main part

manifold

manifolds

semiclassical quantization

simplest class