Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smooth perfectness through decomposition of diffeomorphisms into fiber
  preserving ones   We show that on a closed smooth manifold $M$ equipped with $k$ fiber bundle
structures whose vertical distributions span the tangent bundle, every smooth
diffeomorphism $f$ of $M$ sufficiently close to the identity can be written as
a product $f=f_1... f_k$, where $f_i$ preserves the $i^{\text{th}}$-fiber. The
factors $f_i$ can be chosen smoothly in $f$. We apply this result to show that
on a certain class of closed smooth manifolds every diffeomorphism sufficiently
close to the identity can be written as product of commutators and the factors
can be chosen smoothly. Furthermore we get concrete estimates on how many
commutators are necessary.

35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph