Commutative algebra for cohomology rings of virtual duality groups

Journal of Algebra

Volumn 192, Issue 2, 1997, Pages 678-700

  Benson, D J ^a   Greenlees, J P C ^b  

^a UNIVERSITY OF GEORGIA   (United States)

^b Probability and Statistics Section   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031570627     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1006/jabr.1996.6944     Document Type: Article

References (25)

1. 1. D. J. Benson, "Representations and Cohomology, I," Cambridge Studies in Advanced Mathematics, Vol. 30, Cambridge Univ. Press, 1991.
2. 2. D. J. Benson, "Representations and Cohomology, II," Cambridge Studies in Advanced Mathematics, Vol. 31, Cambridge Univ. Press, 1991.
3. 3. D. J. Benson and J. F. Carlson, Complexity and multiple complexes, Math. Z. 195 (1987), 221-238.
4. 4. D. J. Benson and J. F. Carlson, Projective resolutions and Poincaré duality complexes, Trans. Amer. Math. Soc. 342 (1994), 447-488.
5. 5. D. J. Benson and J. F. Carlson, Functional equations for Poincaré series in group cohomology, Bull. London Math. Soc., 26 (1994), 438-448.
6. 6. D. J. Benson and J. P. C. Greenlees, Commutative algebra for cohomology rings of classifying spaces of compact Lie groups, J. Pure Appl. Algebra, to appear.
7. 7. R. Bieri, "Homological Dimension of Discrete Groups," Queen Mary College Mathematics Notes, 1976.
8. 8. A. Borel, Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts, Ann. of Math. 57 (1953), 115-207.
9. 9. A. Borel and J. P. Serre, Corners and arithmetic groups, Comment. Math. Helv. 48 (1973), 436-491.
10. 10. K. S. Brown, "Cohomology of Groups," Graduate tests in Math., Vol. 87, Springer-Verlag, Berlin/New York, 1982.
11. 11. A. D. Elmendorf, J. P. C. Greenlees, I. Kriz, and J. P. May, Commutative algebra in stable homotopy theory and a completion theory, Math. Res. Lett. 1 (1994), 225-239.
12. 12. A. Elmendorf, I. Kriz, M. Mandell, and J. P. May, Modern foundations for stable homotopy theory, in "Handbook of Topology" (I. M. James, Ed.), pp. 213-253, North-Holland, Amsterdam, 1995.
13. 13. A. Elmendorf, I. Kriz, M. Mandell, and J. P. May, with an appendix by M. Cole, "Rings, Modules and Algebras in Stable Homotopy Theory," Mathematical Surveys and Monographs, Vol. 47, Amer. Math. Soc., Providence, 1997.
14. 14. A. Elmendorf and J. P. May, Algebras over equivariant sphere spectra, J. Pure Appl. Algebra, to appear.
15. 15. J. P. C. Greenlees, The K-homology of universal spaces and local cohomology of the representation ring, Topology 32 (1993), 295-308.
16. 16. J. P. C. Greenlees, Commutative algebra in group cohomology, J. Pure Appl. Algebra 98 (1995), 151-162.
17. 17. J. P. C. Greenlees and J. P. May, Completions in algebra and topology, in "Handbook of Topology" (I. M. James, Ed.), pp. 255-276, North-Holland, Amsterdam, 1995.
18. 18. J. P. C. Greenlees and J. P. May, Equivalent stable homotopy theory, in "Handbook of Topology" (I. M. James, Ed.), pp. 277-323, North-Holland, Amsterdam, 1995.
19. 19. A. Grothendieck (notes by R. Hartshorne), "Local Cohomology," Lecture Notes in Math., Vol. 41, Springer-Verlag, Berlin/New York, 1967.
20. 20. J. L. Harer, The virtual cohomological dimension of the mapping class group of an orientable surface, Invent. Math. 84 (1986), 157-176.
21. 21. W. Harvey, Boundary structure for the modular group, in "Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conferences," Ann. Math. Stud. 97 (1978), 245-251.
22. ∞, J. Pure Appl. Algebra 90 (1993), 55-67.
23. 23. L. G. Lewis, J. P. May, and M. Steinberger (with contributions by J. E. McClure), "Equivariant Stable Homotopy Theory," Lecture Notes in Math., Vol. 1213, Springer-Verlag, Berlin/New York, 1986.
24. 3(ℤ), Topology 17 (1978), 1-22.
25. 25. C. W. Stark, Homologically trivial actions on chain complexes and finiteness properties of infinite groups, J. Pure Appl. Algebra 94 (1994), 217-228.