Synge's theorem

Updated on Nov 09, 2023

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In mathematics, specifically Riemannian geometry, Synge's theorem is a classical result relating the curvature of a Riemannian manifold to its topology. It is named for John Lighton Synge, who proved it in 1936. Let M be a compact Riemannian manifold with positive sectional curvature. The theorem asserts:

If M is even-dimensional and orientable, then M is simply connected.

If M is odd-dimensional, then it is orientable.

References

Synge's theorem Wikipedia

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