On the decomposition of 3-dimensional Poincare duality complexes


John Crisp


Research Report 96-20
Date: 18 April 1996


We show that if the fundamental group of an orientable 3-dimensional Poincare duality complex has infinitely many ends then it is either a proper free product or virtually free of finite rank. It follows that every 3-dimensional Poincare complex is finitely covered by one which is homotopy equivalent to a connected sum of aspherical complexes and copies of S1 X S2. Furthermore, any torsion element of the fundamental group of an orientable 3-dimensional Poincare complex has finite centraliser.

Key phrases

Poincare duality complex. Poincare complex. graph of groups. tree.

AMS Subject Classification (1991)

Primary: 57P10


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