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

Calculating with spaces

Example: "homology" is a "Functor" where a
Space X is sent to a sequence of Vector Spaces
H0(X), H1(X), H2(X), ...
Such functors

Hopf-Poincaré theorem: given a vector field on X
the "wheighted sum" of the indices of the singularities of the field
is equal to
the "Euler characteristic" of X
dim H0(X) - dim H1(X) + dim H2(X) - ...

Bjørn Ian Dundas