Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Factoring Formal Maps into Reversible or Involutive Factors   An element $g$ of a group is called reversible if it is conjugate in the
group to its inverse. An element is an involution if it is equal to its
inverse. This paper is about factoring elements as products of reversibles in
the group $\mathfrak{G}_n$ of formal maps of $(\mathbb{C}^n,0)$, i.e.
formally-invertible $n$-tuples of formal power series in $n$ variables, with
complex coefficients. The case $n=1$ was already understood.
  Each product $F$ of reversibles has linear part $L(F)$ of determinant $\pm1$.
The main results are that for $n\ge2$ each map $F$ with det$(L(F))=\pm1$ is the
product of $2+3c$ reversibles, and may also be factored as the product of
$9+6c$ involutions, where $c$ is the smallest integer $\ge \log_2n$.

29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom