Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vector bundles and Gromov-Hausdorff distance   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.

15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org