Artículos de revistas
Profinite Completions Of Orientable Poincaré Duality Groups Of Dimension Four And Euler Characteristic Zero
Registro en:
Groups, Geometry, And Dynamics. , v. 3, n. 3, p. 401 - 421, 2009.
16617207
2-s2.0-67650538966
Autor
Kochloukova D.H.
Institución
Resumen
Let p be a prime number, T a class of finite groups closed under extensions, subgroups and quotients, and suppose that 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 Poincare duality group G of dimension 4 and Euler characteristic 0 to be a profinite orientable Poincare duality group of dimension 4 at the prime p with Euler p-characteristic 0. In particular we show that the pro-p completion Ĝp of G is an orientable Poincare duality pro- p group of dimension 4 and Euler characteristic 0 if and only if G is p-good. © European Mathematical Society. 3 3 401 421 R. Bieri, Homological dimension of discrete groups. 2nd ed., Queen Mary College Mathematical Notes, Queen Mary College, London 1981. Zbl 0357.20027 MR 0715779K. S. Brown, Cohomology of groups. Graduate Texts in Math. 87, Springer-Verlag, New York 1994. Zbl 0584.20036 MR 1324339Demuškin, S.P., The group of a maximal p-extension of a local field (1961) Izv. Akad. Nauk SSSR Ser. Mat, 25, pp. 329-346. , Zbl 0100.03302 MR 0123565 Demuskin, S.P., On 2-extensions of a local field (1963) Sibirsk. Mat. Zh, 4, pp. 951-955 English transl, (1966) Amer. Math. Soc. Transl. (2), 50, pp. 178-182. , Zbl 0131.27001 MR 0161854 Kochloukova, D.H., Pro-C completions of orientable (2007) PD 3-pairs, , Preprint, Campinas Kochloukova, D.H., Zalesskii, P.A., Profinite and pro-p completions of Poincare duality groups of dimension 3 (2008) Trans. Amer. Math. Soc, 360, pp. 1927-1949. , Zbl 1143.20016 MR 2366969 Korenev, A.A., Pro-p groups with a finite number of ends (2004) Mat. Zametki, 76, pp. 531-538 English transl, (2004) Math. Notes, 76, pp. 490-196. , Zbl 1080.20024 MR 2112069 Korenev, A.A., Cohomology groups of pro-p-groups with coefficients in a group ring and the virtual Poincare duality (2005) Mat. Zametki, 78, pp. 853-863 English transl, (2005) Math. Notes, 78, pp. 791-800. , Zbl 1129.20032 MR 2249035 Labute, J.P., Classification of Demushkin groups (1967) Canad. J. Math, 19, pp. 106-132. , Zbl 0153.04202 MR 0210788 J. Neukirch, A. Schmidt, and K. Wingberg, Cohomology of number fields. Grundlehren Math. Wiss. 323, Springer-Verlag, Berlin 2000. Zbl 0948.11001 MR 1737196Reznikov, A., Three-manifolds class field theory (homology of coverings for a nonvir- tually bi-positive manifold) (1997) Selecta Math. (N.S.), 3, pp. 361-399. , Zbl 0892.57012 MR 1481134 L. Ribes and P. Zalesskii, Profinite groups. Ergeb. Math. Grenzgeb. (3) 40, Springer- Verlag, Berlin 2000. Zbl 0949.20017 MR 1775104J.-P. Serre, Structure de certains pro-p-groupes (d'apres Demuskin). Sem. Bourbaki 15 (1962/63), Exp. No. 252 Sem. Bourbaki, 8, Exp. No. 252, 145-155, Soc. Math. France, Paris 1995. Zbl 0121.04404 MR 1611538J.-P. Serre, Galois cohomology. Springer-Verlag, Berlin 1997. Zbl 0902.12004 MR 1466966P. Symonds and T. Weigel, Cohomology of p-adic analytic groups. In New horizons in pro-p groups, Progr. Math. 184, Birkhäuser, Boston 2000, 349-U0. Zbl 0973.20043 MR 1765127Weigel, T., On profinite groups with finite abelianizations (2007) Selecta Math. (N.S.), 13, pp. 175-181. , Zbl 2330590 MR 2330590