Decompositions of hyperbolic groups

Benjamin Barrett (University of Cambridge)

Wednesday 4th October, 2017 16:00-17:00 Maths 311B


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 geometry of the group and is algebraic decomposition.

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