Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The world problem: on the computability of the topology of 4-manifolds   Topological classification of the 4-manifolds bridges computation theory and
physics. A proof of the undecidability of the homeomorphy problem for
4-manifolds is outlined here in a clarifying way. It is shown that an arbitrary
Turing machine with an arbitrary input can be encoded into the topology of a
4-manifold, such that the 4-manifold is homeomorphic to a certain other
4-manifold if and only if the corresponding Turing machine halts on the
associated input. Physical implications are briefly discussed.

36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph