o:537489
Quasi-isometries between groups with two-ended splittings
en
We construct a ‘structure invariant’ of a one-ended, finitely presented group that describes
the way in which the factors of its JSJ decomposition over two-ended subgroups fit together.
For hyperbolic groups satisfying a very general condition, these invariants completely reduce the problem of classifying such groups up to quasi-isometry to a relative quasi-isometry
classification of the factors of their JSJ decomposition. Under some additional assumption,
our results extend to more general finitely presented groups, yielding a far-reaching generalisation of the quasi-isometry classification of some 3–manifolds obtained by Behrstock and
Neumann.
The same approach also allows us to obtain such a reduction for the problem of determining when two hyperbolic groups have homeomorphic Gromov boundaries.
2017-06-30T13:37:07.775Z
44
yes
46
Christopher
Cashen
Alexandre
Martin
person
application/pdf
630756
http://phaidra.univie.ac.at/o:537489
no
yes
1
70
group splitting, JSJ decomposition, quasi-isometry
1552253