Topologi på roterommet
BID, February 2013 (At h-bar)
1. Is size always important?
2. To comb the hair of a sphere
3. The Euler charcteristic
4. Fusion reactors
5. A flat world?
6. Pacman's universe
7. What is the shape of space?
8. A flat but finite universe
A. State spaces
B. The study of spaces
C. What is a deformation?
D. How to calculate with spaces
For a 2D creature, these are spaces to live in, and if our creature is slightly self-centered, it will never discover that the universe is not the plane.
orientable (e.g. the plane, sphere and torus, where "left" and "right" make sense),others are
non-orientable (e.g., the Klein bottle).What is it like to live on a Klein bottle?
The Klein bottle won't fit in 3D without self-intersections.
3D space is simply to small: in 4D the Klein bottle fits nicely.
Similar phenomenon: the Borromean rings. No two are linked, but together they can't be pulled appart.
However these 3D and 4D spaces have nothing to do with our 2D universe: for 2D creatures these are totally abstract (only occuring in the ravings of theoretical physicists).
A cute book (and a movie) called Flatland is about 2D creatures.