# Hecke structure on Bredon cohomology

Fundamenta Mathematicae (1991)

- Volume: 140, Issue: 1, page 1-30
- ISSN: 0016-2736

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topSłomińska, Jolanta. "Hecke structure on Bredon cohomology." Fundamenta Mathematicae 140.1 (1991): 1-30. <http://eudml.org/doc/211925>.

@article{Słomińska1991,

abstract = {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.},

author = {Słomińska, Jolanta},

journal = {Fundamenta Mathematicae},

keywords = {Hecke functor; Mackey functor; spectral sequence converging to the Bredon cohomology; finite group actions; Hecke structure on equivariant Bredon cohomology with local coefficients; Mackey structure; Illman transfer},

language = {eng},

number = {1},

pages = {1-30},

title = {Hecke structure on Bredon cohomology},

url = {http://eudml.org/doc/211925},

volume = {140},

year = {1991},

}

TY - JOUR

AU - Słomińska, Jolanta

TI - Hecke structure on Bredon cohomology

JO - Fundamenta Mathematicae

PY - 1991

VL - 140

IS - 1

SP - 1

EP - 30

AB - 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.

LA - eng

KW - Hecke functor; Mackey functor; spectral sequence converging to the Bredon cohomology; finite group actions; Hecke structure on equivariant Bredon cohomology with local coefficients; Mackey structure; Illman transfer

UR - http://eudml.org/doc/211925

ER -

## References

top- [1] M. Auslander, Representation theory of artin algebras I, Comm. Algebra 1 (3) (1974), 177-268. Zbl0285.16028
- [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. Zbl0246.57017
- [4] K. S. Brown, Cohomology of Groups, Springer, 1982. Zbl0584.20036
- [5] T. tom Dieck, Equivariant homology and Mackey functors, Math. Ann. 206 (1973), 67-78. Zbl0253.18017
- [6] J. A. Green, Axiomatic representation theory for finite groups, J. Pure Appl. Algebra 1 (1971), 41-77. Zbl0249.20005
- [7] S. Illman, Equivariant singular homology and cohomology I, Mem. Amer. Math. Soc. 156 (1975). Zbl0297.55003
- [8] S. Jackowski and J. E. McClure, Homotopy decomposition of classifying spaces via elementary abelian subgroups, Topology, to appear. Zbl0754.55014
- [9] B. Mitchell, Rings with several objects, Adv. in Math. 8 (1972), 1-161. Zbl0232.18009
- [10] J. Słomińska, Equivariant Bredon cohomology of classifying spaces of families of subgroups, Bull. Acad. Polon. Sci. Sér. Sci. Math. 28 (1980), 503-508. Zbl0479.55006
- [11] J. Słomińska, Finiteness conditions in Bredon cohomology, J. Pure Appl. Algebra, to appear. Zbl0748.55003
- [12] J. Słomińska, Smith theory and quasi-periodicity in Bredon cohomology, in preparation. Zbl0762.55005
- [13] S. Waner, A generalization of cohomology of groups, Proc. Amer. Math. Soc. 85 (1982), 469-474. Zbl0518.57016
- [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.

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