Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The number of smooth 4-manifolds with a fixed complexity   One can define the complexity of a smooth 4-manifold as the minimal sum of
the number of disks, strands and crossings in a Kirby diagram. Martelli proved
that the number of homeomorphism classes of complexity less than n grows as
$n^2$. In this paper we prove that the number of diffeomorphism classes grows
at least as fast as $n^{c\sqrt[3]{n}}$. Along the way we construct complete
kirby diagrams for a large family of knot surgery manifolds.

14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat