Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An estimate for the volume entropy of nonpositively curved graph
  manifolds   Let M be a closed 3-dimensional graph manifold. We prove that h(g)>1 for each
geometrization g of M, where h(g) is the topological entropy of geodesic flow
of g.

19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th