- the state space of two electrons of equal spin
- the space of all lines in
**R**through the origin.^{3}

Build

- take a Möbius band, (whose boundary is a circle) and
- attach a disc.

**R**P^{2}is not orientable- has a fancy "hole".

This hole "disappears" if you go around it twice,

- This hole is also in the
*space of rotations*, giving complications in e.g. aviation.

- If space
**is**a Poincaré sphere, there is such a hole in the universe! **and**another hole which disappears if you go around it 5 times ...

- How do you detect such holes?

Bjørn Ian Dundas