On the decomposition of 3-dimensional Poincare duality complexes
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.
Poincare duality complex. Poincare complex. graph of groups. tree.
AMS Subject Classification (1991)
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Sydney Mathematics and Statistics