Even-dimensional real projective spaces, the Klein bottle, nonorientable surfaces, and the Möbius band are nonorientable.Suggest a slogan
The following manifolds are not orientable: the real projective spaces \(\RP^n\) for \(n\geq 2\) even [@Hat02], the Klein bottle and more generally the closed nonorientable surfaces \(N_k\) [@Hat02], and the open Möbius band.
Which of the standard manifolds are nonorientable?