Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the growth of L2-invariants of locally symmetric spaces, II: exotic
  invariant random subgroups in rank one   In the first paper of this series (arxiv.org/abs/1210.2961) we studied the
asymptotic behavior of Betti numbers, twisted torsion and other spectral
invariants for sequences of lattices in Lie groups G. A key element of our work
was the study of invariant random subgroups (IRSs) of G. Any sequence of
lattices has a subsequence converging to an IRS, and when G has higher rank,
the Nevo-Stuck-Zimmer theorem classifies all IRSs of G. Using the
classification, one can deduce asymptotic statments about spectral invariants
of lattices.
  When G has real rank one, the space of IRSs is more complicated. We construct
here several uncountable families of IRSs in the groups SO(n,1). We give
dimension-specific constructions when n=2,3, and also describe a general gluing
construction that works for every n at least 2. Part of the latter construction
is inspired by Gromov and Piatetski-Shapiro's construction of non-arithmetic
lattices in SO(n,1).

10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an