A Shapiro lemma for diagrams of spaces with applications to equivariant topology

I. Moerdijk; J. A. Svensson

Compositio Mathematica (1995)

  • Volume: 96, Issue: 3, page 249-282
  • ISSN: 0010-437X

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Moerdijk, I., and Svensson, J. A.. "A Shapiro lemma for diagrams of spaces with applications to equivariant topology." Compositio Mathematica 96.3 (1995): 249-282. <http://eudml.org/doc/90363>.

@article{Moerdijk1995,
author = {Moerdijk, I., Svensson, J. A.},
journal = {Compositio Mathematica},
keywords = {homology; equivariant Bredon; twisted coefficients; equivariant Whitehead theorem; Shapiro lemma; diagrams of spaces},
language = {eng},
number = {3},
pages = {249-282},
publisher = {Kluwer Academic Publishers},
title = {A Shapiro lemma for diagrams of spaces with applications to equivariant topology},
url = {http://eudml.org/doc/90363},
volume = {96},
year = {1995},
}

TY - JOUR
AU - Moerdijk, I.
AU - Svensson, J. A.
TI - A Shapiro lemma for diagrams of spaces with applications to equivariant topology
JO - Compositio Mathematica
PY - 1995
PB - Kluwer Academic Publishers
VL - 96
IS - 3
SP - 249
EP - 282
LA - eng
KW - homology; equivariant Bredon; twisted coefficients; equivariant Whitehead theorem; Shapiro lemma; diagrams of spaces
UR - http://eudml.org/doc/90363
ER -

References

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  1. 1 G.E. Bredon, Equivariant Cohomology Theories, SLN34 (1967). Zbl0162.27202MR214062
  2. 2 Th. Bröcker, Singuläre Definition der äquivarianten Bredon homologie, Manus. Math.5 (1971), 91-102. Zbl0213.49902MR293618
  3. 3 K.S. Brown, Cohomology of Groups, Springer-Verlag, 1982. Zbl0584.20036MR672956
  4. 4 T. tom Dieck, Transformation Groups and Representation Theory, SLN766 (1979). Zbl0445.57023MR551743
  5. 5 T. tom Dieck, Transformation Groups, de Gruyter, 1987. Zbl0611.57002MR889050
  6. 6 A. Dold, D. Puppe, Homologie nicht-additiver Funktoren. Anwendungen, Ann. de l'Inst. Fourier11 (1961), 201-312. Zbl0098.36005MR150183
  7. 7 E. Dror Farjoun, Homotopy and homology of diagrams of spaces, in SLN1286 (1987), 93-134. Zbl0659.55011MR922924
  8. 8 E. Dror Farjoun, A.Zabrodsky, Homotopy equivalence between diagrams of spaces, J. Pure Appl. Alg.41 (1986), 169-182. Zbl0612.55017MR849903
  9. 9 W. Dwyer, D.M. Kan, Function complexes for diagrams of simplicial sets, Proc. Kon. Ned. Acad. Wet.86 (= Indag. Math.45) (1983), 139-146. Zbl0555.55018MR705421
  10. 10 W. Dwyer. D.M. Kan, An obstruction theory for diagrams of simplicial sets, Proc. Kon. Ned. Acad. Wet.87 (=Indag. Math.46) (1984), 139-149. Zbl0555.55018MR749527
  11. 11 B. Eckmann, Cohomology of groups and transfers, Ann. Math.58 (1983), 481-493. Zbl0052.02002MR58600
  12. 12 A.D. Elmendorf, Systems of fixed point sets, Trans. A.M.S.277 (1983), 275-284. Zbl0521.57027MR690052
  13. 13 A. Grothendieck, Sur quelques points de l'algèbre homologique, Tôhoku Math J.9 (1957), 119-221. Zbl0118.26104MR102537
  14. 14 P. Gabriel, M. Zisman, Calculus of Fractions and Homotopy Theory, Springer-Verlag, 1967. Zbl0186.56802MR210125
  15. 15 A. Heller, Homotopy theories, Memoirs A.M.S.383 (1988). Zbl0643.55015MR920963
  16. 16 P.J. Hilton, U. Stammbach, A Course in Homological Algebra, Springer-Verlag, 1971. Zbl0238.18006MR346025
  17. 17 L. Illusie, Complexe cotangent et déformations II, SLN283 (1972). Zbl0224.13014MR491681
  18. 18 K. Lamotke, Semi-simpliziale algebraische Topologie, Springer-Verlag, 1968. Zbl0188.28301MR245005
  19. 19 L.G. Lewis, J.P. May, M. Steinberger, Equivariant Stable Homotopy Theory, SLN1213 (1986). Zbl0611.55001
  20. 20 J.P. May, Simplicial Objects in Algebraic Topology, Van Nostrand, 1967 (reprinted by Univ. of Chicago Press, 1982). Zbl0565.55001MR222892
  21. 21 I. Moerdijk, J.A. Svensson, The equivariant Serre spectral sequence, Proc. A.M.S.118 (1993), 263-278. Zbl0791.55004MR1123662
  22. 22 J.M. Møller, On equivariant function spaces, Pacific J. Math.142 (1990), 103-119. Zbl0673.55012MR1038731
  23. 23 M.Y. Oruç, The equivariant Steenrod algebra, Top. Appl.32 (1989), 77-108. Zbl0675.55010MR1003301
  24. 24 D. Quillen, Higher algebraic K-theory I, in SLN341 (1973), 85-147. Zbl0292.18004MR338129
  25. 25 R.M. Seymour, Some functorial constructions on G-spaces, Bull. London Math. Soc.15 (1983), 353-359. Zbl0519.57035MR703760
  26. 26 J S⋖omińska, On the equivariant Chern homomorphism, Bull. de l'Acad. Pol. Sci. 24 (1976), 909-913. Zbl0343.55003
  27. 27 R.W. Thomason, Homotopy colimits in the category of small categories, Math. Proc. Camb. Phil. Soc.85 (1979), 91-109. Zbl0392.18001MR510404
  28. 28 F. Waldhausen, Algebraic K-theory of spaces, in SLN1126 (1985), 318-419. Zbl0579.18006MR802796
  29. 29 A. Weil, Sur la théorie du corps de classes, J. Math. Soc. Japan3 (1951), 1-35 (see footnote p 12). Zbl0044.02901MR44569

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