Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Enriched Riemann Sphere, Morse Stability and Equi-singularity in
  $\mathcal{O}_2$   The \textit{Enriched Riemann Sphere} $\C P_*^1$ is $\C P^1$ plus a set of
\textit{infinitesimals}, having the Newton-Puiseux field $\F$ as coordinates.
Complex Analysis is extended to the $\F$-\textit{Analysis}
(\textit{Newton-Puiseux Analysis}). The classical \textit{Morse Stability
Theorem} is also extended; the \textit{stability idea} is used to formulate an
\textit{equi-singular deformation theorem} in $\C\{x,y\}(=\mathcal{O}_2)$.

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The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
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The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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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: solv-int
1
The categories of this paper are: cs