On the Homotopy Classification of Elliptic Operators on Manifolds with Edges

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

2005-03-29

arxiv.org/abs/math/0503694v1

Mathematics

Operator Algebras

Scientific paper

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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