Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orderings and flexibility of some subgroups of $Homeo_+(\mathbb{R})$   In this work we exhibit flexibility phenomena for some (countable) groups
acting by order preserving homeomorphisms of the line. More precisely, we show
that if a left orderable group admits an amalgam decomposition of the form
$G=\mathbb{F}_n*_{\mathbb Z} \mathbb{F}_m$ where $n+m\geq 3$, then every
faithful action of $G$ on the line by order preserving homeomorphisms can be
approximated by another action (without global fixed points) that is not
semi-conjugated to the initial action. We deduce that $\mathcal{LO}(G)$, the
space of left orders of $G$, is a Cantor set.
  In the special case where $G=\pi_1(\Sigma)$ is the fundamental group of a
closed hyperbolic surface, we found finer techniques of perturbation. For
instance, we exhibit a single representation whose conjugacy class in dense in
the space of representations. This entails that the space of representations
without global fixed points of $\pi_1(\Sigma)$ into $Homeo_+(\mathbb R)$ is
connected, and also that the natural conjugation action of $\pi_1(\Sigma)$ on
$\mathcal{LO}(\pi_1(\Sigma))$ has a dense orbit.

13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
18
The categories of this paper are: econ