Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the o-minimal Hilbert's fifth problem   Let ${\mathbb M}$ be an arbitrary o-minimal structure. Let $G$ be a definably
compact definably connected abelian definable group of dimension $n$. Here we
compute the new the intrinsic o-minimal fundamental group of $G;$ for each
$k>0$, the $k$-torsion subgroups of $G;$ the o-minimal cohomology algebra over
${\mathbb Q}$ of $G.$ As a corollary we obtain a new uniform proof of Pillay's
conjecture, an o-minimal analogue of Hilbert's fifth problem, relating
definably compact groups to compact real Lie groups, extending the proof
already known in o-minimal expansions of ordered fields.

1
The categories of this paper are: cs
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas