Hecke structure on Bredon cohomology

Jolanta Słomińska

Fundamenta Mathematicae (1991)

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

Abstract

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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.

How to cite

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Słomińska, 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

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  1. [1] M. Auslander, Representation theory of artin algebras I, Comm. Algebra 1 (3) (1974), 177-268. Zbl0285.16028
  2. [2] G. E. Bredon, Equivariant Cohomology Theory, Lecture Notes in Math. 34, Springer, 1967. 
  3. [3] G. E. Bredon, Introduction to Compact Transformation Groups, Academic Press, 1972. Zbl0246.57017
  4. [4] K. S. Brown, Cohomology of Groups, Springer, 1982. Zbl0584.20036
  5. [5] T. tom Dieck, Equivariant homology and Mackey functors, Math. Ann. 206 (1973), 67-78. Zbl0253.18017
  6. [6] J. A. Green, Axiomatic representation theory for finite groups, J. Pure Appl. Algebra 1 (1971), 41-77. Zbl0249.20005
  7. [7] S. Illman, Equivariant singular homology and cohomology I, Mem. Amer. Math. Soc. 156 (1975). Zbl0297.55003
  8. [8] S. Jackowski and J. E. McClure, Homotopy decomposition of classifying spaces via elementary abelian subgroups, Topology, to appear. Zbl0754.55014
  9. [9] B. Mitchell, Rings with several objects, Adv. in Math. 8 (1972), 1-161. Zbl0232.18009
  10. [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. [11] J. Słomińska, Finiteness conditions in Bredon cohomology, J. Pure Appl. Algebra, to appear. Zbl0748.55003
  12. [12] J. Słomińska, Smith theory and quasi-periodicity in Bredon cohomology, in preparation. Zbl0762.55005
  13. [13] S. Waner, A generalization of cohomology of groups, Proc. Amer. Math. Soc. 85 (1982), 469-474. Zbl0518.57016
  14. [14] S. Waner, Mackey functors and G-cohomology, ibid. 90 (1984), 641-648. 
  15. [15] T. Yoshida, On G-functors. I, Hokkaido Math. J. 9 (1980), 222-257. 
  16. [16] T. Yoshida, On G-functors. II, J. Math. Soc. Japan 35 (1983), 179-190. 

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