Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounded generation and lattices that cannot act on the line   Let D be an irreducible lattice in a connected, semisimple Lie group G with
finite center. Assume that the real rank of G is at least two, that G/D is not
compact, and that G has more than one noncompact simple factor. We show that D
has no orientation-preserving actions on the real line. (In algebraic terms,
this means that D is not right orderable.) Under the additional assumption that
no simple factor of G is isogenous to SL(2,R), applying a theorem of E.Ghys
yields the conclusion that any orientation-preserving action of D on the circle
must factor through a finite, abelian quotient of D.
  The proof relies on the fact, proved by D.Carter, G.Keller, and E.Paige, that
SL(2,A) is boundedly generated by unipotents whenever A is a ring of integers
with infinitely many units. The assumption that G has more than one noncompact
simple factor can be eliminated if all noncocompact lattices in SL(3,R) and
SL(3,C) are virtually boundedly generated by unipotents.

8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th