Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subspace stabilisers in hyperbolic lattices   This paper shows that immersed totally geodesic $m$-dimensional suborbifolds
of $n$-dimensional arithmetic hyperbolic orbifolds correspond to finite
subgroups of the commensurator whenever $m \geqslant \lfloor \frac{n}{2}
\rfloor$. We call such totally geodesic suborbifolds finite centraliser
subspaces (or fc-subspaces) and use them to formulate an arithmeticity
criterion for hyperbolic lattices.
  We show that a hyperbolic orbifold $M$ is arithmetic if and only if it has
infinitely many fc-subspaces, and provide examples of non-arithmetic orbifolds
that contain non-fc subspaces of codimension one. We analyse the relation
between Vinberg's commensurability invariants of an arithmetic hyperbolic
orbifold and those of its totally geodesic suborbifolds, provide an algebraic
characterisation of totally geodesic immersions of hyperbolic orbifolds, and
use it to construct examples of totally geodesic immersions of arithmetic
hyperbolic orbifolds with different adjoint trace fields and ambient groups of
different types. We also provide examples of $3$-dimensional arithmetic
hyperbolic orbifolds which cannot be geodesically immersed in higher
dimensional arithmetic ones.
  Finally, we study arithmetic properties of orbifolds that descend to their
totally geodesic suborbifolds, proving that all suborbifolds in a
(quasi)-arithmetic orbifold are (quasi)-arithmetic.

16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga