This is a preview of subscription content, log in via an institution to check access.
References
[Ad]Adams, J. F., Maps between classifying spaces, II.Invent. Math., 49 (1978), 1–65.
[AS]Atiyah, M. &Segal, G. EquivariantK-theory and completion.J. Differential Geom., 3 (1969), 1–18.
[At]Atiyah, M., Bott periodicity and the index of elliptic operators.Quart. J. Math. Oxford Ser. (2), 19 (1968), 113–140.
[AT]Atiyah, M. &Tall, D., Group representations, λ-rings and theJ-homomorphism.Topology, 8 (1969), 253–297.
[BK]Bousfield, A. &Kan, D. Homotopy Limits, Completions, and Localizations. Lecture Notes in Math., 304. Springer-Verlag, Berlin-New York, 1972 [1987].
[Br]Bredon, G. Introduction to Compact Transformation Groups. Academic Press, New York-London, 1972.
[DZ]Dwyer, W. &Zabrodsky, A., Maps between classifying spaces, inAlgebraic Topology, Barcelona, 1986. Lecture Notes in Math., 1298, pp. 106–119. Springer-Verlag, Berlin-New York, 1987.
[FM]Friedlander, E. &Mislin, G., Locally finite approximations of Lie groups, I.Invent. Math., 83 (1986), 425–436.
[Ja]Jackowski, S., Group homomorphisms inducing isomorphisms of cohomology.Topology, 17 (1978), 303–307.
[JM1]Jackowski, S. &McClure, J., Homotopy approximations for classifying spaces of compact Lie groups, inAlgebraic Topology, Arcata, CA, 1986. Lecture Notes in Math., 1370, pp. 221–234. Springer-Verlag, Berlin-New York, 1989.
[JM2] —, Homotopy decomposition of classifying spaces via elementary abelian subgroups.Topology, 31 (1992), 113–132.
[JMO]Jackowski, S., McClure, J. &Oliver, B., Homotopy classification of self-maps ofBG viaG-actions.Ann. of Math., 135 (1992), 183–270.
[JMO2] — Homotopy theory of classifying spaces of compact Lie groups, inAlgebraic Topology and Its Applications, pp. 81–123. Math. Sci. Res. Inst. Publ., 27. Springer-Verlag, New York, 1994.
[JMO3]Jackowski, S. Maps between classifying spaces revisited. Submitted toProceedings of the Cech Centennial Homotopy Theory Conference (AMS Contemp. Math. series).
[LMM]Lewis, L. G., May, J. P. &McClure, J., OrdinaryRO(G)-graded cohomology.Bull. Amer. Math. Soc., 4 (1981), 208–212.
[Mi]Miller, H., The Sullivan conjecture on maps from classifying spaces.Ann. of Math., 120 (1984), 39–87.
[MS]McDuff, D. &Segal, G., Homology fibrations and the “group-completion” theorem.Invent. Math., 31 (1976), 279–284.
[MSt]Milnor, J. &Stasheff, J.,Characteristic Classes. Ann. of Math. Studies, 76. Princeton Univ. Press, Princeton, NJ, 1974.
[Nb]Notbohm, D., Maps between classifying spaces.Math. Z., 207 (1991), 153–168.
[O1]Oliver, B., A transfer for compact Lie group actions.Proc. Amer. Math. Soc., 97 (1986), 546–548.
[O2] —, Higher limits via Steinberg representations.Comm. Algebra, 22 (1994), 1381–1393.
[O3]Oliver, B., The representation ring of a compact Lie group revisited. In preparation.
[Se]Segal, G., The representation ring of a compact Lie group.Inst. Hautes Études Sci. Publ. Math., 34 (1968), 113–128.
[tD]Dieck, T. tom,Transformation Groups. de Gruyter Stud. Math., 8 de Gruyter, Berlin-New York, 1987.
[Wo]Wojtkowiak, Z., On maps from holimF toZ, inAlgebraic Topology, Barcelona, 1986. Lecture Notes in Math., 1298, pp. 227–236. Springer-Verlag, Berlin-New York, 1987.
Author information
Authors and Affiliations
Additional information
The first author was partly supported by Polish Scientific Grant 2P30101007.
Rights and permissions
About this article
Cite this article
Jackowski, S., Oliver, B. Vector bundles over classifying spaces of compact Lie groups. Acta Math. 176, 109–143 (1996). https://doi.org/10.1007/BF02547337
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02547337