The equivariant Serre spectral sequence

Moerdijk, I.; Svensson, J.-A.

doi:10.1090/S0002-9939-1993-1123662-9

The equivariant Serre spectral sequence

Authors: I. Moerdijk and J.-A. Svensson
Journal: Proc. Amer. Math. Soc. 118 (1993), 263-278
MSC: Primary 55T10; Secondary 55N91, 55R91, 55T99
DOI: https://doi.org/10.1090/S0002-9939-1993-1123662-9
MathSciNet review: 1123662
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Abstract: For spaces with a group action, we introduce Bredon cohomology with local (or twisted) coefficients and show that it is invariant under weak equivariant homotopy equivalence. We use this new cohomology to construct a Serre spectral sequence for equivariant fibrations.

[1] Glen E. Bredon, Equivariant cohomology theories, Lecture Notes in Mathematics, No. 34, Springer-Verlag, Berlin-New York, 1967. MR 0214062
[2] Theodor Bröcker, Singuläre Definition der äquivarianten Bredon Homologie, Manuscripta Math. 5 (1971), 91–102 (German, with English summary). MR 0293618, https://doi.org/10.1007/BF01397610
[3] Albrecht Dold and Dieter Puppe, Homologie nicht-additiver Funktoren. Anwendungen, Ann. Inst. Fourier Grenoble 11 (1961), 201–312 (German, with French summary). MR 0150183
[4] A. D. Elmendorf, Systems of fixed point sets, Trans. Amer. Math. Soc. 277 (1983), no. 1, 275–284. MR 690052, https://doi.org/10.1090/S0002-9947-1983-0690052-0
[5] P. Gabriel and M. Zisman, Calculus of fractions and homotopy theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 35, Springer-Verlag New York, Inc., New York, 1967. MR 0210125
[6] John W. Gray, Fibred and cofibred categories, Proc. Conf. Categorical Algebra (La Jolla, Calif., 1965) Springer, New York, 1966, pp. 21–83. MR 0213413
[7] Alexander Grothendieck, Sur quelques points d’algèbre homologique, Tôhoku Math. J. (2) 9 (1957), 119–221 (French). MR 0102537, https://doi.org/10.2748/tmj/1178244839
[8] I. Moerdijk and J.-A. Svensson, A Shapiro lemma for diagrams of spaces, with applications to equivariant topology (to appear).
[9] Daniel Quillen, Higher algebraic 𝐾-theory. I, Algebraic 𝐾-theory, I: Higher 𝐾-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972) Springer, Berlin, 1973, pp. 85–147. Lecture Notes in Math., Vol. 341. MR 0338129
[10] Graeme Segal, Categories and cohomology theories, Topology 13 (1974), 293–312. MR 0353298, https://doi.org/10.1016/0040-9383(74)90022-6
[11] R. M. Seymour, Some functional constructions on 𝐺-spaces, Bull. London Math. Soc. 15 (1983), no. 4, 353–359. MR 703760, https://doi.org/10.1112/blms/15.4.353
[12] R. W. Thomason, Homotopy colimits in the category of small categories, Math. Proc. Cambridge Philos. Soc. 85 (1979), no. 1, 91–109. MR 510404, https://doi.org/10.1017/S0305004100055535
[13] Charles E. Watts, A homology theory for small categories, Proc. Conf. Categorical Algebra (La Jolla, Calif., 1965) Springer, New York, 1966, pp. 331–335. MR 0204497