Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Liftable vector fields, unfoldings and augmentations   We study liftable vector fields of smooth map-germs. We show how to obtain
the module of liftable vector fields of any map-germ of finite singularity type
from the module of liftable vector fields of a stable unfolding of it. As an
application, we obtain the liftable vector fields for the family $H_k$ in
Mond's list. We then show the relation between the liftable vector fields of a
stable germ and its augmentations.

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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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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: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: physics