Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On uniqueness of JSJ decompositions of finitely generated groups   We give an example of two JSJ decompositions of a group that are not related
by conjugation, conjugation of edge-inclusions, and slide moves. This answers
the question of Rips and Sela stated in "Cyclic splittings of finitely
presented groups and the canonical JSJ decomposition," Ann. of Math. 146
(1997), 53-109.
  On the other hand we observe that any two JSJ decompositions of a group are
related by an elementary deformation, and that strongly slide-free JSJ
decompositions are genuinely unique. These results hold for the decompositions
of Rips and Sela, Dunwoody and Sageev, and Fujiwara and Papasoglu, and also for
accessible decompositions.

16
The categories of this paper are: stat
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci