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Hopf formulas for equivariant integral homology of groups
Author(s):
Hvedri
Inassaridze;
Emzar
Khmaladze
Journal:
Proc. Amer. Math. Soc.
138
(2010),
3037-3046.
MSC (2010):
Primary 18G10, 18G50
Posted:
April 21, 2010
MathSciNet review:
2653928
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Additional information
Abstract:
By using purely algebraic methods of  -fold Čech derived functors, the higher equivariant integral group homology is investigated from the Hopf formulas point of view.
References:
-
- 1.
- M. Barr and J. Beck, Homology and standard constructions, Lecture Notes in Mathematics, Vol. 80, Springer-Verlag, Berlin/New York (1969), 245-335. MR 0258917 (41:3562)
- 2.
- R. Brown and G. J. Ellis, Hopf formulae for the higher homology of a group, Bull. London Math. Soc. 20 (1988), 124-128. MR 924238 (89g:20082)
- 3.
- G. Carlsson, Equivariant stable homotopy theory and related areas, in: G. Carlsson (ed.), Proc. Workshop at Stanford University, 2000, Homology Homotopy Appl. 3 (2) (2001), vii-xv. MR 1856027
- 4.
- J. M. Casas, N. Inassaridze, E. Khmaladze and M. Ladra, Homology of (n+1)-types and Hopf type formulas, J. Pure Appl. Algebra 200 (2005), 267-280. MR 2147270 (2006b:18014)
- 5.
- A.M. Cegarra, J.M. Garcia-Calcines, and J.A. Ortega, Cohomology of groups with operators, Homology Homotopy Appl. 4 (1) (2002), 1-23. MR 1894065 (2003c:20064)
- 6.
- A.M. Cegarra and H. Inassaridze, Homology of groups with operators, Int. Math. J. 5 (1) (2004), 29-48. MR 2031933
- 7.
- G. Donadze, N. Inassaridze and T. Porter,
 -Fold Čech derived functors and generalised Hopf type formulas,  -theory 35 (2003), 341-373. MR 2240237 (2007d:18022) - 8.
- J. Duskin, Simplicial methods and the interpretation of ``triple'' cohomology, Mem. Amer. Math. Soc. 3 (1975), no. 163. MR 0393196 (52:14006)
- 9.
- G.J. Ellis and R. Steiner, Higher-dimensional crossed modules and the homotopy groups of
 -ads, J. Pure Appl. Algebra 46 (1987), 117-136. MR 897011 (88j:55010) - 10.
- Z. Fiedorowicz, H. Hauschild and J.P. May, Equivariant K-theory, Lecture Notes in Math., 967, Springer, Berlin, 1982, 23-80. MR 689388 (84h:57023)
- 11.
- H. Inassaridze, Equivariant homology and cohomology of groups, Topology and its Application, 153 (2005), 66-89. MR 2172035 (2006e:18020)
- 12.
- N. Inassaridze,
 -fold Čech derived functors of group valued functors, Bull. Georgian Acad. Sci. 168 (2) (2003). - 13.
- A. Kuku, Equivariant K-theory and the cohomology of profinite groups, Algebraic
 -Theory, Number Theory, Geometry and Analysis, in: Lecture Notes in Math., 342, Springer, Berlin, 1984, 235-244. MR 750684 (86h:18005) - 14.
- J.-L. Loday, Spaces with finitely many nontrivial homotopy groups, J. Pure Appl. Algebra 24 (1982), 179-202. MR 651845 (83i:55009)
- 15.
- N.C. Philips, Equivariant K-theory and freeness of group actions on C*-algebras, Lecture Notes in Math., 1274, Springer, Berlin, 1987. MR 911880 (89k:46086)
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Additional Information:
Hvedri
Inassaridze
Affiliation:
Department of Algebra, A. Razmadze Mathematical Institute, M. Alexidze St. 1, 0193 Tbilisi, Georgia - and - Tbilisi Centre for Mathematical Sciences, Tbilisi, Georgia
Email:
hvedri@rmi.acnet.ge
Emzar
Khmaladze
Affiliation:
Department of Algebra, A. Razmadze Mathematical Institute, M. Alexidze St. 1, 0193 Tbilisi, Georgia - and - Tbilisi Centre for Mathematical Sciences, Tbilisi, Georgia
Email:
khmal@rmi.acnet.ge
DOI:
10.1090/S0002-9939-10-10381-5
PII:
S 0002-9939(10)10381-5
Keywords:
Hopf formula,
equivariant homology,
cotriple homology,
projective simplicial resolution,
crossed $n$-cube,
\v {C}ech derived functor.
Received by editor(s):
July 10, 2009
Posted:
April 21, 2010
Additional Notes:
The authors were supported by the Volkswagen Foundation, Ref.: I/84 328, INTAS, Ref.: 06-1000017-8609; and the Georgian National Science Foundation, Ref.: ST06/3-004.
Communicated by:
Alexander N. Dranishnikov
Copyright of article:
Copyright
2010,
American Mathematical Society
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