Hecke structure on Bredon cohomology

• Autorzy: Jolanta Słomińska
• Języki publikacji: EN

Abstrakty

EN

We construct a Hecke structure on equivariant Bredon cohomology with local coefficients and then describe some of its properties. We compare this structure with the Mackey structure defined by T. tom Dieck and with the Illman transfer.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1991-1992
• Tom: 140
• Numer: 1
• Strony: 1-30

Daty

wydano

1991

otrzymano

1990-02-07

poprawiono

1990-10-15

Twórcy

autor

Jolanta Słomińska

• Institute of Mathematics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Bibliografia

• [1] M. Auslander, Representation theory of artin algebras I, Comm. Algebra 1 (3) (1974), 177-268.
• [2] G. E. Bredon, Equivariant Cohomology Theory, Lecture Notes in Math. 34, Springer, 1967.
• [3] G. E. Bredon, Introduction to Compact Transformation Groups, Academic Press, 1972.
• [4] K. S. Brown, Cohomology of Groups, Springer, 1982.
• [5] T. tom Dieck, Equivariant homology and Mackey functors, Math. Ann. 206 (1973), 67-78.
• [6] J. A. Green, Axiomatic representation theory for finite groups, J. Pure Appl. Algebra 1 (1971), 41-77.
• [7] S. Illman, Equivariant singular homology and cohomology I, Mem. Amer. Math. Soc. 156 (1975).
• [8] S. Jackowski and J. E. McClure, Homotopy decomposition of classifying spaces via elementary abelian subgroups, Topology, to appear.
• [9] B. Mitchell, Rings with several objects, Adv. in Math. 8 (1972), 1-161.
• [10] J. Słomińska, Equivariant Bredon cohomology of classifying spaces of families of subgroups, Bull. Acad. Polon. Sci. Sér. Sci. Math. 28 (1980), 503-508.
• [11] J. Słomińska, Finiteness conditions in Bredon cohomology, J. Pure Appl. Algebra, to appear.
• [12] J. Słomińska, Smith theory and quasi-periodicity in Bredon cohomology, in preparation.
• [13] S. Waner, A generalization of cohomology of groups, Proc. Amer. Math. Soc. 85 (1982), 469-474.
• [14] S. Waner, Mackey functors and G-cohomology, ibid. 90 (1984), 641-648.
• [15] T. Yoshida, On G-functors. I, Hokkaido Math. J. 9 (1980), 222-257.
• [16] T. Yoshida, On G-functors. II, J. Math. Soc. Japan 35 (1983), 179-190.