When studying a group, it is natural and often useful to try to cut it up
onto simpler pieces. Sometimes this can be done in an entirely canonical
way analogous to the JSJ decomposition of a 3-manifold, in which the
collection of tori along which the manifold is cut is unique up to isotopy.
It is a theorem of Brian Bowditch that if the group acts nicely on a metric
space with a negative curvature property then a canonical decomposition can
be read directly from the large-scale geometry of that space. In this talk
we shall explore an algorithmic consequence of this relationship between
the large-scale geometry of the group and is algebraic decomposition.
- Topology Seminar