Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Clustering polar curves   This essay builds on the idea of grouping the polar curves of 2-variable
function germs into polar clusters. In the topological category, one obtains a
bijective correspondence between certain partitions of the polar quotients of
two topologically equivalent function germs. We explain how this bijective
correspondence may be refined in the Lipschitz category in terms of the
associated gradient canyons.

36
The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
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The categories of this paper are: eess