Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiplicity, regularity and blow-spherical equivalence of real analytic
  sets   This article is devoted to studying multiplicity and regularity of real
analytic sets. We present an equivalence for real analytic sets, named
blow-spherical equivalence, which generalizes differential equivalence and
subanalytic bi-Lipschitz equivalence and, with this approach, we obtain several
applications on analytic sets. On regularity, we show that blow-spherical
regularity of real analytic implies $C^1$ smoothness only in the case of real
analytic curves. On multiplicity, we present a generalization for Gau-Lipman's
Theorem about differential invariance of the multiplicity in the complex and
real cases, we show that the multiplicity ${\rm mod}\,2$ is invariant by
blow-spherical homeomorphisms in the case of real analytic curves and surfaces
and also for a class of real analytic foliations and is invariant by (image)
arc-analytic blow-spherical homeomorphisms in the case of real analytic
hypersurfaces, generalizing some results proved by G. Valette. We present also
a complete classification of the germs of real analytic curves.

6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph