# On the decomposition of 3-dimensional Poincare duality complexes

## Author

**John Crisp**

## Status

Research Report 96-20

Date: 18 April 1996

## Abstract

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

Secondary:

## Content

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