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The decomposition of 3-dimensional Poincaré complexes
Author(s) -
John Crisp
Publication year - 2000
Publication title -
commentarii mathematici helvetici
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.603
H-Index - 46
eISSN - 1420-8946
pISSN - 0010-2571
DOI - 10.1007/pl00000372
Subject(s) - mathematics , decomposition , poincaré conjecture , pure mathematics , mathematical analysis , ecology , biology
. 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.

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