Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solvability in Groups of Piecewise-linear Homeomorphisms of the Unit
  Interval   We investigate subgroups of the group PLo(I) of piecewise-linear, orientation
preserving homeomorphisms of the unit interval with finitely many breaks in
slope, and also subgroups of Thompson's group F. We find geometric criteria
determining the derived length of any such group, and use this criteria to
classify the solvable and non-solvable subgroups of PLo(I) and of F.
  Let H be a subgroup of PL_o(I) or F. We find that H is solvable if and only
if H is isomorphic to a group in a well described class R of groups. We also
find that H is non-solvable if and only if we can embed a copy of a specific
non-solvable group W into H.
  We strengthen the non-solvability classification by finding weak geometric
criteria under which we can embed other groups (all containing W) into
non-solvable subgroups of PLo(I) or F.

21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat