2004/03/31 by A. Savin, Anton Savin
Mathematics · #Advanced Operator Algebra Research #Homotopy and Cohomology in Algebraic Topology #Spectral Theory in Mathematical Physics #math.AP #math.KT #math.OA #msc:19K33 #msc:35S35 #msc:47L15 #msc:58J05
paper · pdf · doi:10.1007/s10977-005-1515-1
published as K-Theory, Vol. 34, No. 1. (January 2005), pp. 71-98 · revised version; 25 pages; section with applications expanded
openalex publication_date 2005/01/01 · arxiv created 2005/03/13 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.