Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Structure and regularity of group actions on one-manifolds   In this monograph, we give an account of the relationship between the
algebraic structure of finitely generated and countable groups and the
regularity with which they act on manifolds. We concentrate on the case of
one--dimensional manifolds, culminating with a uniform construction of finitely
generated groups acting with prescribed regularity on the compact interval and
on the circle. We develop the theory of dynamical obstructions to smoothness,
beginning with classical results of Denjoy, to more recent results of Kopell,
and to modern results such as the $abt$--Lemma. We give a classification of the
right-angled Artin groups that have finite critical regularity and discuss
their exact critical regularities in many cases, and we compute the virtual
critical regularity of most mapping class groups of orientable surfaces.

21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int