Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lusin Approximation and Horizontal Curves in Carnot Groups   We show that, given an absolutely continuous horizontal curve $\gamma$ in the
Heisenberg group, there is a $C^1$ horizontal curve $\Gamma$ such that
$\Gamma=\gamma$ and $\Gamma'=\gamma'$ outside a set of small measure.
Conversely, we construct an absolutely continuous horizontal curve in the Engel
group with no $C^1$ horizontal approximation.

23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: eess
3
The categories of this paper are: physics
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The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat