|
Comparison of the discrete and continuous cohomology groups of a pro- group
Author(s):
G.
A.
Fernández-Alcober;
I.
V.
Kazachkov;
V.
N.
Remeslennikov;
P.
Symonds
Original publication:
Algebra i Analiz,
tom 19
(2007),
nomer 6.
Journal:
St. Petersburg Math. J.
19
(2008),
961-973.
MSC (2000):
Primary 20J06
Posted:
August 22, 2008
MathSciNet review:
2411962
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
It is studied whether or not the natural map from the continuous to the discrete second cohomology group of a finitely generated pro- group is an isomorphism.
References:
-
- 1.
- J. Barwise (ed.), Handbook of mathematical logic, Stud. Logic Found. Math., vol. 90, North-Holland, Amsterdam, 1977. MR 0457132 (56:15351)
- 2.
- A. K. Bousfield, On the
 -adic completions of nonnilpotent spaces, Trans. Amer. Math. Soc. 331 (1992), 335-359. MR 1062866 (92g:55014) - 3.
- K. S. Brown, Cohomology of groups, Grad. Texts in Math., vol. 87, Springer-Verlag, New York-Berlin, 1982. MR 0672956 (83k:20002)
- 4.
- H. Cartan et al., Algèbres d'Eilenberg-MacLane et homotopie, Séminaire Henri Cartan, 7e année: 1954/55, École Normale Supérieure, Paris, 1956. MR 0087935 (19:439a)
- 5.
- J. D. Dixon, M. P. F. du Sautoy, A. Mann, and D. Segal, Analytic pro-
 groups, 2nd ed., Cambridge Stud. Adv. Math., vol. 61, Cambridge Univ. Press, Cambridge, 1999. MR 1720368 (2000m:20039) - 6.
- E. M. Friedlander and G. Mislin, Cohomology of classifying spaces of complex Lie groups and related discrete groups, Comment. Math. Helv. 59 (1984), 347-361. MR 0761803 (86j:55011)
- 7.
- S. MacLane, Homology, Grundlehren Math. Wiss., Bd. 114, Springer-Verlag, Berlin-New York, 1967. MR 0349792 (50:2285)
- 8.
- J. Milnor, On the homology of Lie groups made discrete, Comment. Math. Helv. 58 (1983), 72-85. MR 0699007 (85b:57050)
- 9.
- G. Mislin, private communication, 1997.
- 10.
- L. Ribes and P. Zalesskii, Profinite groups, Ergeb. Math. Grenzgeb. (3), Bd. 40, Springer-Verlag, Berlin, 2000. MR 1775104 (2001k:20060)
- 11.
- J.-P. Serre, Cohomologie galoisienne, Lecture Notes in Math., vol. 5, Springer-Verlag, Berlin-New York, 1965. MR 0201444 (34:1328)
- 12.
- B. Sury, Central extensions of p-adic groups; a theorem of Tate, Comm. Algebra 21 (1993), 1203-1213. MR 1209928 (93m:19002)
- 13.
- J. S. Wilson, Profinite groups, London Math. Soc. Monogr. New Ser., vol. 19, The Clarendon Press, Oxford Univ. Press, New York, 1998. MR 1691054 (2000j:20048)
Similar Articles:
Retrieve articles in St. Petersburg Mathematical Journal
with MSC
(2000):
20J06
Retrieve articles in all Journals with MSC
(2000):
20J06
Additional Information:
G.
A.
Fernández-Alcober
Affiliation:
Matematika Saila, Zientzia eta Teknologia Fakultatea, Euskal Herriko Unibertsitatea, 48080 Bilbao, Spain
Email:
gustavo.fernandez@ehu.es
I.
V.
Kazachkov
Affiliation:
Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St. West, Montreal, Quebec H3A 2K6, Canada
Email:
kazachkov@math.mcgill.ca
V.
N.
Remeslennikov
Affiliation:
Institute of Mathematics, Russian Academy of Sciences, Pevtsova St. 13, 644099 Omsk, Russia
Email:
remesl@iitam.omsk.net.ru
P.
Symonds
Affiliation:
School of Mathematics, University of Manchester, P.O. Box 88, Manchester M60 1QD, United Kingdom
Email:
peter.symonds@manchester.ac.uk
DOI:
10.1090/S1061-0022-08-01030-3
PII:
S 1061-0022(08)01030-3
Keywords:
Profinite group,
comparison map
Received by editor(s):
15/JUL/2007
Posted:
August 22, 2008
Additional Notes:
The first author was supported by the Spanish Ministry of Science and Education, grant MTM2004-04665, partly with FEDER funds, and by the University of the Basque Country, grant UPV05/99.
The third author was supported by the RFBR, grant no.~05-01-00057
Dedicated:
To the memory of D. K. Faddeev
Copyright of article:
Copyright
2008,
American Mathematical Society
|
