Abstract

Using asymptotic morphisms between graded C^*-algebras, we construct for every open m-dimensional spin manifold M a fundamental class in the m-th analytic K-homology group of M. This class is associated to the not necessarily essentially self-adjoint Dirac operator on M. A careful treatment is given of the main properties of these fundamental K-homology classes.

Keywords

asymptotic morphisms, analytic K-homology, E-theory, Real C*-algebras, Dirac operators

Mathematical Subject Classification

Primary: 19K33

Secondary: 19K35, 46L80

Authors