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Locally symmetric homology spheres and an application of Matsushima's formula

Published online by Cambridge University Press:  24 October 2008

Francis E. A. Johnson
Francis E. A. Johnson
Affiliation:
University College, London
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Extract

It is a matter of some interest to determine which closed manifolds have the same homology as a closed aspherical manifold (7) (9). This paper is concerned with the more restrictive question of which spheres have the same homology as some closed aspherical manifold.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 91 , Issue 3 , May 1982 , pp. 459 - 466
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

REFERENCES

(1)Borel, A.Topics in the homology theory of fibre bundles (Lecture Notes in Mathematics, Springer-Verlag, 1967).CrossRefGoogle Scholar
(2)Borel, A.Density properties of certain subgroups of semisimple groups. Ann. of Math. 72 (1960), 179–188.CrossRefGoogle Scholar
(3)Borel, A. and Wallace, N. Seminar on the cohomology of discrete subgroups of semi simple Lie groups. Mimeographed notes. Institute for Advanced Study.Google Scholar
(4)Chevalley, C.The Betti numbers of the exceptional simple Lie groups. Proc. Int. Cong. Math. 1950. vol. 11, pp. 21–24.Google Scholar
(5)Griffiths, P. A. and Harris, J.Principles of algebraic geometry (Wiley Interscience, 1978).Google Scholar
(6)Helgason, S.Differential geometry, Lie groups and symmetric spaces (Academic Press, 1978).Google Scholar
(7)Johnson, F. E.A. Two conjectures in the theory of Poincare' Duality groups. Proc. Amer. Math. Soc. 81 (1981), 353–354.Google Scholar
(8)Johnson, F. E. A.Aspherical manifolds of standard linear type. Math. Ann. 255 (1981), 303–316.CrossRefGoogle Scholar
(9)Kan, D. M. and Thurston, W. P.Every connected space has the homology of a K(π, 1). Topology 15 (1976), 253–258.Google Scholar
(10)Matsushima, Y.A formula for the Betti numbers of compact locally symmetric Riemannian manifolds. J. Diff. Geom. 1 (1967), 99–109.Google Scholar
(11)Schmid, W.Vanishing theorems for Lie algebra cohomology and the cohomology of discrete subgroups of semisimple Lie groups. Advances in Math. 41 (1981), 78–113.CrossRefGoogle Scholar
(12)Serre, J. P. Cohomologie des groupes discrets. In Prospects in mathematics. Ann. of Math. Studies, no. 70 (Princeton University Press, 1971).Google Scholar
(13)Spanier, E.Algebraic topology (McGraw-Hill, 1966).Google Scholar
(14)Zuckerman, G.Continuous cohomology and unitary representations of real reductive groups. Ann. of Math. 107 (1978), 495–516.CrossRefGoogle Scholar