Follow the question, how do we characterize a generic unorientable 2d manifolds (whose the first stiefel whitney class of the tangent bundle is nonzero)?
For example, for a generic orientable 2d manifolds, we can use
- the genus $g$
- the Euler character $\chi=2-2g$
How about the full characterization and characters of a generic unorientable 2d manifolds?
If you have comments on higher dimensions (3d, 4d, 5d, etc), this will also be welcome too.