Groups, Geometry, and Dynamics


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Volume 3, Issue 3, 2009, pp. 401–421
DOI: 10.4171/GGD/64

Published online: 2009-09-30

Profinite completions of orientable Poincaré duality groups of dimension four and Euler characteristic zero

Dessislava H. Kochloukova[1]

(1) IMECC - UNICAMP, Campinas, Brazil

Let p be a prime number, T be a class of finite groups closed under extensions, subgroups and quotients and the cyclic group of order p is in T.

We find some sufficient and necessary conditions for the pro-T completion of an abstract orientable Poincaré duality group G of dimension 4 and Euler characteristic 0 to be a profinite orientable Poincaré duality group of dimension 4 at the prime p with Euler p-characteristic 0. In particular we show that the pro-p completion \hat{G}p of G is an orientable Poincaré duality pro-p group of dimension 4 and Euler characteristic 0 if and only if G is p-good.

Keywords: Poincaré duality group, profinite completion, p-good group

Kochloukova Dessislava: Profinite completions of orientable Poincaré duality groups of dimension four and Euler characteristic zero. Groups Geom. Dyn. 3 (2009), 401-421. doi: 10.4171/GGD/64