Preissmann's theorem: Difference between revisions
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{{in all dimensions}} | {{in all dimensions}} | ||
{{relating curvature to topology}} | |||
==Statement== | ==Statement== | ||
Let <math>M</math> be a compact Riemannian manifold with negative sectional curvature everywhere. Then, every nontrivial Abelian subgroup of the fundamental group of <math>M</math> is infinite cyclic. | Let <math>M</math> be a compact Riemannian manifold with negative sectional curvature everywhere. Then, every nontrivial Abelian subgroup of the fundamental group of <math>M</math> is infinite cyclic. | ||
Revision as of 08:38, 22 June 2007
This result is valid in all dimensions
This result relates information on curvature to information on topology of a manifold
Statement
Let be a compact Riemannian manifold with negative sectional curvature everywhere. Then, every nontrivial Abelian subgroup of the fundamental group of is infinite cyclic.
