Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Profinite rigidity of graph manifolds, II: knots and mapping classes   In this paper we study some consequences of the author's classification of
graph manifolds by their profinite fundamental groups. In particular we study
commensurability, the behaviour of knots, and relation to mapping classes. We
prove that the exteriors of graph knots are distinguished among all 3-manifold
groups by their profinite fundamental groups. We also prove a strong conjugacy
separability result for certain mapping classes of surfaces.

12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys