Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some exotic nontrivial elements of the rational homotopy groups of
  $\mathrm{Diff}(S^4)$   This paper studies the rational homotopy groups of the group
$\mathrm{Diff}(S^4)$ of self-diffeomorphisms of $S^4$ with the
$C^\infty$-topology. We present a method to prove that there are many `exotic'
non-trivial elements in $\pi_*\mathrm{Diff}(S^4)\otimes \mathbb{Q}$
parametrized by trivalent graphs. As a corollary of the main result, the
4-dimensional Smale conjecture is disproved. The proof utilizes Kontsevich's
characteristic classes for smooth disk bundles and a version of clasper surgery
for families. In fact, these are analogues of Chern--Simons perturbation theory
in 3-dimension and clasper theory due to Goussarov and Habiro.

18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg