Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cone fields and topological sampling in manifolds with bounded curvature   Often noisy point clouds are given as an approximation of a particular
compact set of interest. A finite point cloud is a compact set. This paper
proves a reconstruction theorem which gives a sufficient condition, as a bound
on the Hausdorff distance between two compact sets, for when certain offsets of
these two sets are homotopic in terms of the absence of {\mu}-critical points
in an annular region. Since an offset of a set deformation retracts to the set
itself provided that there are no critical points of the distance function
nearby, we can use this theorem to show when the offset of a point cloud is
homotopy equivalent to the set it is sampled from. The ambient space can be any
Riemannian manifold but we focus on ambient manifolds which have nowhere
negative curvature. In the process, we prove stability theorems for
{\mu}-critical points when the ambient space is a manifold.

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The categories of this paper are: eess
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The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph