Asymptotic morphisms, K-homology and Dirac operators

Dorin Dumitraşcu

Vol. 218 (2005), No. 1, 53–74

DOI: 10.2140/pjm.2005.218.53

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 2000

Primary: 19K33

Secondary: 19K35, 46L80

Milestones

Received: 13 November 2000

Revised: 3 January 2003

Published: 1 January 2005