N-fold Čech derived functors and generalised Hopf type formulas

K-Theory

Volumn 35, Issue 3-4, 2005, Pages 341-373

  Donadze, Guram ^a   Inassaridze, Nick ^a   Porter, Timothy ^b  

^a A RAZMADZE MATHEMATICAL INSTITUTE   (Georgia)

^b BANGOR UNIVERSITY   (United Kingdom)

Author keywords

ech derived functors; Hopf type formulas; K functors

Indexed keywords

EID: 33744801094     PISSN: 09203036     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10977-005-3115-5     Document Type: Article

References (36)

1. Bogley, W. and Gutierrez, M.: Mayer-Vietoris sequence in homotopy of 2-complexes and in homology of groups, J. Pure Appl. Algebra 77 (1992), 39-65.
2. Barr, M. and Beck, J:. Homology and Standard Constructions, Lecture Notes in Math. 80, Springer-Verlag, Berlin 1969, pp. 245-335.
3. Baues, H.-J. and Conduché, E.: The Central Series for Peiffer Commutators in Groups with Operators, J. Algebra 133 (1) (1990), 1-34.
4. Beyl, F. R. and Tappe, J.: Group extensions, Representations and the Schur Multiplicator, Lecture Notes in Math. 958, Springer-Verlag, Berlin, 1982.
5. Brown, R. and Ellis, G. J.: Hopf formulae for the higher homology of a group, Bull. London Math. Soc. 20 (1988), 124-128.
6. Brown, R. and Loday, J.-L.: Van Kampen theorems for diagrams of spaces, Topology 26 (1987), 311-335.
7. Brown, R. and Loday, J.-L.: Homotopical excision, and Hurewicz theorems, for n-cubes of spaces, Proc. London Math. Soc. 54 (3) (1987), 176-192.
8. Burns, J. and Ellis, G. J.: On the nilpotent multipliers of a group, Math. Z. 226 (3) (1997), 405-428.
9. Conduché, D.: Modules Croisés Géné ralisés de Longueur 2, J. Pure Appl. Algebra 34 (1984), 155-178.
10. Conduché, D.: Letter to Brown, R. and Loday, J.-L. 1984.
11. Conrad, B. Crossed n-fold extensions of groups, n-fold extensions of modules, and higher multipliers, J. Pure Appl. Algebra 36 (1985), 225-235.
12. Ellis, G. J. Relative derived contravariant functors and the cohomology of groups, J. Pure Appl. Algebra 64 (1990) 21-33. (see also the erratum which can be found at http://hamilton.nuigalway.ie on Ellis's preprint list)
13. Ellis, G. L. and Steiner, R.: Higher dimensional crossed modules and the homotopy groups of (n+1)-ads, J. Pure Appl. Algebra 46 (1987), 117-136.
14. Hall, P. The classification of prime-power groups, J. Reine Angew. Math. 182 (1940), 130-141.
15. Inassaridze, H. Non-abelian Homological Algebra and its Applications, Kluwer Academic Publishers, Amsterdam, 1997.
16. Inassaridze, N. and Khmaladze, E.: More about homological properties of precrossed modules, Homology, Homotopy and Applications, 2(7) (2000), 105-114.
17. Janelidze, G.: What is a double central extension? (the question was asked by Ronald Brown), Cahiers de Topologie et Geometrie Differentielle Categorique XXXII-3 (1991), 191-202.
18. Janelidze, G. and Kelly, G. M. Galois theory and a general notion of a central extension, J. Pure Appl. Algebra 97 (1994), 135-161.
19. Kapranov, M. and Saito, M. Hidden Stasheff polytopes in algebraic K-theory and in the space of Morse functions, Contemp. Math. 227 (1999), 191-225.
20. Keune, F. Derived functors and algebraic K-theory, Lecture Notes in Math. 341, Springer-Verlag, 1973, pp. 158-168.
21. Keune, F. Multirelative K -theory and axioms for the K -theory of rings, K-theory, Preprint Archives 137 (1996) (http://www.math.uiuc.edu/K-theory/).
22. Ladra, M. and Grandjeán, A.R.: Crossed modules and homology, J. Pure Appl. Algebra 95 (1994), 41-55.
23. Leedham-Green, C. and McKay, S.: Baer invariants, isologism, varietal laws and homology, Acta Math. 137 (1976), 99-150.
24. Loday, J.-L.: Spaces with finitely many non-trivial homotopy groups, J. Pure Appl. Algebra 24 (1982), 179-202.
25. Loday, J.-L. Homotopical Syzygies, in"Une dégustation topologique: Homotopy theory in the Swiss Alps", Contemporary Mathematics 265 (2000), 99-127.
26. Mutlu, A. and Porter, T.: Iterated Peiffer pairings in the Moore complex of a simplicial group, Applied Categorical Structures 9 (2001), 111-130.
27. Mutlu, A. and Porter, T.: Applications of Peiffer pairings in the Moore complex of a simplicial group, Theory and Applications of Categories 4 (7) (1998), 148-173.
28. Mutlu, A. and Porter, T.: Crossed squares and 2-crossed modules, preprint, Bangor, 2002.
29. Pirashvili, T.: On non-abelian derived functors, Proc. A.Razmadze Math. Inst., Georgian Acad. Sci. 42 (1979), 91-104 (in Russian).
30. Pirashvili, T.: Spectral sequence for epimorphism. I, Proc. Math. Inst. Tbilisi 70 (1982), 69-91 (in Russian).
31. Pirashvili, T.: Simplicial degrees of functors, Math. Proc. Camb. Phil. Soc. 126 (1999), 45-62.
32. Porter, T.: n-types of simplicial groups and crossed n-cubes, Topology, 32 (1) (1993), 5-24.
33. Quillen, D.: Spectral sequences of a double semi-simplicial group, Topology 5 (1966), 155-157.
34. 2n(G), Publ. Mat. Univ. Aut. Barcelona 30 (1986), 77-82.
35. Shatz, S.: Profinite Groups, Arithmetic, and Geometry, Princeton Univ. Press, Princeton, 1972.
36. Stöhr, R.: A generalized Hopf formula for higher homology groups, Comment. Math. Helvetici 64 (1989), 187-199.