A note on the fundamental group of a manifold of negative curvature
1978 ◽
Vol 83
(3)
◽
pp. 415-417
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Keyword(s):
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.
1999 ◽
Vol 60
(3)
◽
pp. 521-528
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2001 ◽
Vol 25
(3)
◽
pp. 183-195
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1985 ◽
Vol 39
(1)
◽
pp. 49-60
Keyword(s):
2009 ◽
Vol 51
(3)
◽
pp. 579-592
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2008 ◽
Vol 60
(6)
◽
pp. 1201-1218
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1993 ◽
Vol 13
(2)
◽
pp. 335-347
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1988 ◽
Vol 8
(2)
◽
pp. 215-239
◽
2004 ◽
Vol 15
(04)
◽
pp. 369-391
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