On the cohomology of generalized homogeneous spaces
HTML articles powered by AMS MathViewer
- by J. P. May and F. Neumann PDF
- Proc. Amer. Math. Soc. 130 (2002), 267-270 Request permission
Abstract:
We observe that work of Gugenheim and May on the cohomology of classical homogeneous spaces $G/H$ of Lie groups applies verbatim to the calculation of the cohomology of generalized homogeneous spaces $G/H$, where $G$ is a finite loop space or a $p$-compact group and $H$ is a “subgroup” in the homotopical sense.References
- Paul F. Baum, On the cohomology of homogeneous spaces, Topology 7 (1968), 15–38. MR 219085, DOI 10.1016/0040-9383(86)90012-1
- P. Hebroni, Sur les inverses des éléments dérivables dans un anneau abstrait, C. R. Acad. Sci. Paris 209 (1939), 285–287 (French). MR 14
- Saunders MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771–782. MR 19, DOI 10.2307/2371335
- W. G. Dwyer and C. W. Wilkerson, Homotopy fixed-point methods for Lie groups and finite loop spaces, Ann. of Math. (2) 139 (1994), no. 2, 395–442. MR 1274096, DOI 10.2307/2946585
- V. K. A. M. Gugenheim and J. Peter May, On the theory and applications of differential torsion products, Memoirs of the American Mathematical Society, No. 142, American Mathematical Society, Providence, R.I., 1974. MR 0394720
- Igor Kříž and J. P. May, Operads, algebras, modules and motives, Astérisque 233 (1995), iv+145pp (English, with English and French summaries). MR 1361938
- J. P. May, The cohomology of principal bundles, homogeneous spaces, and two-stage Postnikov systems, Bull. Amer. Math. Soc. 74 (1968), 334–339. MR 239596, DOI 10.1090/S0002-9904-1968-11947-0
- Frank Neumann, On the cohomology of homogeneous spaces of finite loop spaces and the Eilenberg-Moore spectral sequence, J. Pure Appl. Algebra 140 (1999), no. 3, 261–287. MR 1704440, DOI 10.1016/S0022-4049(98)00013-9
- Frank Neumann, Torsion in the cohomology of finite loop spaces and the Eilenberg-Moore spectral sequence, Topology Appl. 100 (2000), no. 2-3, 133–150. MR 1733040, DOI 10.1016/S0166-8641(98)00094-7
- David L. Rector, Subgroups of finite dimensional topological groups, J. Pure Appl. Algebra 1 (1971), no. 3, 253–273. MR 301734, DOI 10.1016/0022-4049(71)90021-1
Additional Information
- J. P. May
- Affiliation: Department of Mathematics, The University of Chicago, Chicago, Illinois 60637
- MR Author ID: 121750
- Email: may@math.uchicago.edu
- F. Neumann
- Affiliation: Mathematisches Institut der Georg-August-Universität, Göttingen, Germany
- MR Author ID: 606804
- Email: neumann@uni-math.gwdg.de
- Received by editor(s): May 19, 2000
- Published electronically: July 25, 2001
- Additional Notes: The first author was partially supported by the NSF
- Communicated by: Ralph Cohen
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 267-270
- MSC (2000): Primary 55T20, 57T15, 57T35; Secondary 55P35, 55P45
- DOI: https://doi.org/10.1090/S0002-9939-01-06372-9
- MathSciNet review: 1855645