Profinite completions of orientable Poincaré duality groups of dimension four and Euler characteristic zero
Dessislava H. Kochloukova
IMECC - UNICAMP, Campinas, Brazil
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Abstract
Let be a prime number, be a class of finite groups closed under extensions, subgroups and quotients and the cyclic group of order is in .
We find some sufficient and necessary conditions for the pro- completion of an abstract orientable Poincaré duality group of dimension 4 and Euler characteristic 0 to be a profinite orientable Poincaré duality group of dimension 4 at the prime with Euler -characteristic 0. In particular we show that the pro- completion of is an orientable Poincaré duality pro- group of dimension 4 and Euler characteristic 0 if and only if is -good.
Cite this article
Dessislava H. Kochloukova, Profinite completions of orientable Poincaré duality groups of dimension four and Euler characteristic zero. Groups Geom. Dyn. 3 (2009), no. 3, pp. 401–421
DOI 10.4171/GGD/64