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A note on the fundamental group of a manifold of negative curvature

Published online by Cambridge University Press:  24 October 2008

J. C. Wood
J. C. Wood
Affiliation:
Department of Pure Mathematics, University of Leeds
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Extract

Let Y be a compact connected C∞ Riemannian manifold with negative sectional curvatures. Let G be a non-trivial subgroup of the fundamental group π1(Y). G is known to be cyclic if it is abelian (Preissmann (6)) or contains a subnormal abelian (hence cyclic) subgroup (Yau(9)). These results may be generalized as follows: Say that a group G is of type (α) if ∃a ∈ G, a ≠ e, such that for all b belonging to a set of generators for G we have ambn = bqap for some integers m, n, p, q with either m = p or n = q.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 83 , Issue 3 , May 1978 , pp. 415 - 417
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

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