Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thick hyperbolic 3-manifolds with bounded rank   We construct a geometric decomposition for the convex core of a thick
hyperbolic 3-manifold M with bounded rank. Corollaries include upper bounds in
terms of rank and injectivity radius on the Heegaard genus of M and on the
radius of any embedded ball in the convex core of M.

7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio