Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cocompact lattices in complete Kac-Moody groups with Weyl group
  right-angled or a free product of spherical special subgroups   Let G be a complete Kac-Moody group of rank n \geq 2 over the finite field of
order q, with Weyl group W and building \Delta. We first show that if W is
right-angled, then for all q \neq 1 mod 4 the group G admits a cocompact
lattice \Gamma which acts transitively on the chambers of \Delta. We also
obtain a cocompact lattice for q =1 mod 4 in the case that \Delta is Bourdon's
building. As a corollary of our constructions, for certain right-angled W and
certain q, the lattice \Gamma has a surface subgroup. We also show that if W is
a free product of spherical special subgroups, then for all q, the group G
admits a cocompact lattice \Gamma with \Gamma a finitely generated free group.
Our proofs use generalisations of our results in rank 2 concerning the action
of certain finite subgroups of G on \Delta, together with covering theory for
complexes of groups.

0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph