Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Note On Non-Isolated Real Singularities and Links   For analytic map germs $f: (\mathbb{R}^n, 0)\to (\mathbb{R}, 0)$ having an
isolated critical value in the origin with $\dim V(f)>0$ and satisfying the
transversality property of D.B. Massey we show that for $c>0$ a large enough
constant, and $k$ a large enough natural number the local Milnor-L\^e fibers of
$f$ and of the isolated singularity $g=f-c(\sum_{i=1}^n x_i^2)^k$ satisfies the
following. There exists a homotopy equivalence between the negative Milnor-L\^e
fiber of $f$, to which a cobordism between its boundary and the link of $f$ has
been adjoined, and the negative Milnor-L\^e fiber of $g$.

9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat