On an extension of localization theorem and generalized Conner conjecture
HTML articles powered by AMS MathViewer
- by Satya Deo, Tej Bahadur Singh and Ram Anugrah Shukla PDF
- Trans. Amer. Math. Soc. 269 (1982), 395-402 Request permission
Abstract:
Let $G$ be a compact Lie group. Then Borel-Segal-Quillen-Hsiang localization theorems are known for any $G$-space $X$ where $X$ is any compact Hausdorff space or a paracompact Hausdorff space of finite cohomology dimension. The Conner conjecture proved by Oliver and its various generalizations by Skjelbred are also known for only these two classes of spaces. In this paper we extend all of these results for the equivariant category of all finitistic $G$-spaces. For the case when $G = {Z_p}$ or $G = T$ (torus) some of these results were already proved by Bredon.References
-
M. Atiyah and G. Segal, Equivariant $K$-theory, Lecture Notes, Univ. Warwick, 1965.
- Glen E. Bredon, Sheaf theory, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1967. MR 0221500
- Glen E. Bredon, Cohomological aspects of transformation groups, Proc. Conf. on Transformation Groups (New Orleans, La., 1967) Springer, New York, 1968, pp. 245–280. MR 0244990
- Glen E. Bredon, Introduction to compact transformation groups, Pure and Applied Mathematics, Vol. 46, Academic Press, New York-London, 1972. MR 0413144
- Glen E. Bredon, Fixed point sets of actions on Poincaré duality spaces, Topology 12 (1973), 159–175. MR 331375, DOI 10.1016/0040-9383(73)90004-9
- Armand Borel, Seminar on transformation groups, Annals of Mathematics Studies, No. 46, Princeton University Press, Princeton, N.J., 1960. With contributions by G. Bredon, E. E. Floyd, D. Montgomery, R. Palais. MR 0116341
- P. E. Conner, Retraction properties of the orbit space of a compact topological transformation group, Duke Math. J. 27 (1960), 341–357. MR 163987
- Satya Deo and Hari Shankar Tripathi, Compact Lie group actions on finitistic spaces, Topology 21 (1982), no. 4, 393–399. MR 670743, DOI 10.1016/0040-9383(82)90019-2 R. Godement, Théorie des faisceaux, Actualités Sci. Indust., Hermann, Paris, 1952.
- Wu-yi Hsiang, Cohomology theory of topological transformation groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 85, Springer-Verlag, New York-Heidelberg, 1975. MR 0423384
- Robert Oliver, A proof of the Conner conjecture, Ann. of Math. (2) 103 (1976), no. 3, 637–644. MR 415650, DOI 10.2307/1970955
- Daniel Quillen, The spectrum of an equivariant cohomology ring. I, II, Ann. of Math. (2) 94 (1971), 549–572; ibid. (2) 94 (1971), 573–602. MR 298694, DOI 10.2307/1970770 T. Skjelbred, Acyclic orbit space and cohomology eigenvalues of equivariant maps, Preprint No. 8, Oslo, 1975.
- Tor Skjelbred, Cohomology eigenvalues of equivariant mappings, Comment. Math. Helv. 53 (1978), no. 4, 634–642. MR 511853, DOI 10.1007/BF02566104
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 269 (1982), 395-402
- MSC: Primary 57S10
- DOI: https://doi.org/10.1090/S0002-9947-1982-0637697-0
- MathSciNet review: 637697