Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonnegative Ricci curvature, small linear diameter growth and finite
  generation of fundamental groups   In 1968, Milnor conjectured that a complete noncompact manifold with
nonnegative Ricci curvature has a finitely generated fundamental group. The
author applies the Excess Theorem of Abresch and Gromoll (1990), to prove two
theorems. The first states that if such a manifold has small linear diameter
growth then its fundamental group is finitely generated. The second states that
if such a manifold has an infinitely generated fundamental group then it has a
tangent cone at infinity which is not polar. A corollary of either theorem is
the fact that if such a manifold has linear volume growth, then its fundamental
group is finitely generated.

25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph