New York Journal of Mathematics
Volume 5 (1999) 53-81


Navin Keswani

Geometric K-Homology and Controlled Paths

Published: June 14, 1999
Keywords: K-homology, Dirac-type operator, Finite-propagation speed, Trace class operators
Subject: 19K56, 46L80

We show that K-homologous differential operators on an oriented, Riemannian manifold M can be connected by a "controlled path'' of operators. The analytic properties of these paths allows us to measure a winding number (in the sense of de la Harpe and Skandalis). To aid in the exposition we develop a variant of Baum's (M,E,f) model for K-homology. Our model removes the need for Spinc structures in the description of geometric K-homology.

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