Sheaf theory and Paschke duality
K-Theory and Homology
2012-10-25 v1
Abstract
Paschke duality identifies the K-homology of a space X with the K-theory of a certain dual C*-algebra. We show that Paschke's dual algebra is in a natural way the algebra of sections of a certain sheaf of C*-algebras over X, which can be thought of as a sheaf of noncommutative symbols. This conceptually simplifies a number of constructions in K-homology, such as the association of a homology class to an elliptic operator and the construction of assembly maps.
Cite
@article{arxiv.1210.6420,
title = {Sheaf theory and Paschke duality},
author = {John Roe and Paul Siegel},
journal= {arXiv preprint arXiv:1210.6420},
year = {2012}
}