|Covid-19|Synge's theorem Wikipedia
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.