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A rational invariant for certain infinite discrete groups

Published online by Cambridge University Press:  24 October 2008

F. E. A. Johnson
F. E. A. Johnson
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT
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Extract

We introduce a rational-valued invariant which is capable of distinguishing between the commensurability classes of certain discrete groups, namely, the fundamental groups of smooth closed orientable aspherical manifolds of dimensional 4k(k ≥ 1) whose Euler characteristic χ(Λ) is non-zero. The invariant in question is the quotient

where Sign (Λ) is the absolute value of the signature of the intersection form

and [Λ] is a generator of H4k(Λ; ℝ).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 113 , Issue 3 , May 1993 , pp. 473 - 478
Copyright
Copyright © Cambridge Philosophical Society 1993

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References

REFERENCES

[1]Atiyah, M. F.. The signature of fibre bundles. In Collected Papers in Honour of K. Kodaira (Tokyo University Press, 1969), pp. 73–84.Google Scholar
[2]Hirzebruch, F.. The signature of ramified coverings. In Collected Papers in Honour of K. Kodaira (Tokyo University Press, 1969), pp. 253–265.Google Scholar
[3]Kodaira, K.. A certain type of irregular algebraic surface. J. Analyse Math. 19 (1967), 207–215.CrossRefGoogle Scholar
[4]Mostow, G. B. and Siu, Y. T.. A compact Kähler surface of negative curvature not covered by the ball. Ann. of Math. 112 (1980), 321–360.CrossRefGoogle Scholar