Vector bundles and Gromov-Hausdorff distance
By Marc Rieffel. 2006
62 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f6cc5e5e501bc708bda0ef58c150ed962b3afbaf
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In Algebra and Number Theory
In Mathematical Physics
Citations in the corpus
- The Modular Gromov-Hausdorff Propinquity (2013, background): “We shall observe, at the conclusion of this paper, that Rie ffel proved in [40] that the finite dimensional Leibniz quantum compact metric spaces which appear in Corollar y (5.”