Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Persistent homology and microlocal sheaf theory   We interpret some results of persistent homology and barcodes (in any
dimension) with the language of microlocal sheaf theory. For that purpose we
study the derived category of sheaves on a real finite-dimensional vector space
V. By using the operation of convolution, we introduce a pseudo-distance on
this category and prove in particular a stability result for direct images.
Then we assume that V is endowed with a closed convex proper cone $\gamma$ with
non empty interior and study $\gamma$-sheaves, that is, constructible sheaves
with microsupport contained in the antipodal to the polar cone (equivalently,
constructible sheaves for the $\gamma$-topology). We prove that such sheaves
may be approximated (for the pseudo-distance) by "piecewise linear"
$\gamma$-sheaves. Finally we show that these last sheaves are constant on
stratifications by $\gamma$-locally closed sets, an analogue of barcodes in
higher dimension.

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The categories of this paper are: supr-con
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph