Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A triangulation of semi-algebraic sets concerning an analytical
  condition for shortest-length curves   This paper concerns an analytical stratification question of real algebraic
and semi-algebraic sets. For Whitney's stratification in 1957, it partitions a
real algebraic set into partial algebraic manifolds\cite{W}. In 1975 Hironaka
reproved that a real algebraic set is triangulable and also generalized it to
semi-algebraic sets, following the idea of Lojasiewicz's triangulation of
semi-analytic sets in 1964. Following their examples and wondering how geometry
looks like locally. this paper tries to come up with a stratification, in
particular a cell decomposition, such that it satisfies the following
analytical property. Given any shortest curve between two points in a real
algebraic or semi-algebraic set, it interacts each cell (or simplex) at most
finitely many times.

24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph