Elliptic operators on manifolds with singularities and K-homology

Details Elliptic operators on manifolds with singularities and K-homology Elliptic operators on manifolds with singularities and K-homology

2004-03-20

arxiv.org/abs/math/0403335v2

K-Theory, Vol. 34, No. 1. (January 2005), pp. 71-98

Mathematics

Operator Algebras

revised version; 25 pages; section with applications expanded

Scientific paper

10.1007/s10977-005-1515-1

It is well known that elliptic operators on a smooth compact manifold are classified by K-homology. We prove that a similar classification is also valid for manifolds with simplest singularities: isolated conical points and fibered boundary. The main ingredients of the proof of these results are: an analog of the Atiyah-Singer difference construction in the noncommutative case and an analog of Poincare isomorphism in K-theory for our singular manifolds. As applications we give a formula in topological terms for the obstruction to Fredholm problems on manifolds with singularities and a formula for K-groups of algebras of pseudodifferential operators.

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