Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A generalization of Zakalyukin's lemma, and symmetries of surface
  singularities   Zakalyukin's lemma asserts that the coincidence of the images of two wave
front germs implies the right equivalence of corresponding map germs under a
certain genericity assumption. The purpose of this paper is to give an
improvement of this lemma for frontals. Moreover, we give several applications
for singularities on surfaces.

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The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys