TOPOLOGICAL INVARIANTS AND CURVATURE

Gholam Hossein Arab, Megerdich Toomanian

Abstract


It is widely known that the fundamental group of a Lie group, and in general a symmetric space, is abelian. In the current paper it is demonstrated that any finitely generated abelian group is the fundamental group of a compact Lie group.            In addition, it is proved that for any arbitrary group there is a differentiable manifold of dimension greater than 3 whose fundamental group is that arbitrary group.




Keywords


Lie groups;Fundamental group;Finitely generated abelian groups;Homotopy groups;Sectional curvature

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