Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinitely many hyperbolic Coxeter groups through dimension 19   We prove the following: there are infinitely many finite-covolume (resp.
cocompact) Coxeter groups acting on hyperbolic space H^n for every n < 20
(resp. n < 7). When n=7 or 8, they may be taken to be nonarithmetic.
Furthermore, for 1 < n < 20, with the possible exceptions n=16 and 17, the
number of essentially distinct Coxeter groups in H^n with noncompact
fundamental domain of volume less than or equal to V grows at least
exponentially with respect to V. The same result holds for cocompact groups for
n < 7. The technique is a doubling trick and variations on it; getting the most
out of the method requires some work with the Leech lattice.

20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
18
The categories of this paper are: econ
16
The categories of this paper are: stat