Commentarii Mathematici Helvetici
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Published online: 2000-06-30
The decomposition of 3-dimensional Poincaré complexesJ. Crisp (1) Université de Bourgogne, Dijon, France
We show that if the fundamental group of an orientable PD3-complex has infinitely many ends then it is either a proper free product or virtually free of finite rank. It follows that every PD3-complex is finitely covered by one which is homotopy equivalent to a connected sum of aspherical PD3-complexes and copies of $ S^1 \times S^2 $. Furthermore, it is shown that any torsion element of the fundamental group of an orientable PD3-complex has finite centraliser.
Keywords: Poincaré complex, graph of groups, tree
Crisp J.: The decomposition of 3-dimensional Poincaré complexes. Comment. Math. Helv. 75 (2000), 232-246. doi: 10.1007/PL00000372