JSJ Decompositions
Edited by Mladen Bestvina, Kent Morrison, Panagiotis Papazoglou, and ichard Scott
Splitting theory of groups parallels decomposition theorems in
3-manifold theory. Kneser’s theorem has its analog in Grushko’s
theorem, Haken finiteness and hierarchies gave rise to
accessibility and strong accessibility in group theory while JSJ
decompositions of 3-manifolds were shown recently to extend to
group theory too. One should stress that these "generalizations"
from 3-manifolds to groups were by no means routine and a lot of
questions remain open today. The structure theory that one obtains
for groups is often much more general that the 3-manifold theory
and it had many striking applications (isomorphism problem for
hyperbolic groups, Tarski problems etc). We refer to
[MR1469317] and [MR1664694] for the basic definitions.
Sections
Cite this as: AimPL: JSJ Decompositions, available at http://aimpl.org/jsjdecomp.