Spheres, tori, orientable surfaces, odd-dimensional real projective spaces, and lens spaces are orientable.Suggest a slogan
The following closed manifolds are orientable: the spheres \(S^n\) and tori \(T^n\) for \(n\geq 1\), the closed orientable surfaces \(\Sigma_g\), the real projective spaces \(\RP^n\) for \(n\) odd, and the lens spaces [@Hat02].
Which of the standard manifolds are orientable?