Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recovering the homology of immersed manifolds   Given a sample of an abstract manifold immersed in some Euclidean space, we
describe a way to recover the singular homology of the original manifold. It
consists in estimating its tangent bundle---seen as subset of another Euclidean
space---in a measure theoretic point of view, and in applying measure-based
filtrations for persistent homology. The construction we propose is consistent
and stable, and does not involve the knowledge of the dimension of the
manifold.In order to obtain quantitative results, we introduce the normal
reach, which is a notion of reach suitable for an immersed manifold.

29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th