%0 Journal Article
%T Vector bundles and Gromov-Hausdorff distance
%A Marc A. Rieffel
%J Mathematics
%D 2006
%I arXiv
%X We show how to make precise the vague idea that for compact metric spaces that are close together for Gromov-Hausdorff distance, suitable vector bundles on one metric space will have counterpart vector bundles on the other. Our approach employs the Lipschitz constants of projection-valued functions that determine vector bundles. We develop some computational techniques, and we illustrate our ideas with simple specific examples involving vector bundles on the circle, the two-torus, the two-sphere, and finite metric spaces. Our topic is motivated by statements concerning "monopole bundles" over matrix algebras in the literature of theoretical high-energy physics.
%U http://arxiv.org/abs/math/0608266v4