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

En flate med to hull som kan embeddes i tre dimensjonertorussphereplan

Other 2D universes

2D: only a few universes.

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.

Klein flaske En tur på Mobius' bånd Some spaces are
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.

To og to henger ringene ikke sammen, men rommet er trangt! 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.

Bjørn Ian Dundas