Hi people,

I'm interested in results, such as the Gauß-Bonnet theorem, Fàry-Milnor theorem or classification theorems for manifolds, which give topological properties from geometric considerations. Can anyone recommend some good texts? In particular I'd like to see a nice proof of Fàry-Milnor and of the theorem of turning tangents (total curvature of an imbedded plane curve is $2\pi$).

thanks

knottedclosed curve in $\mathbb R^2$ is at least $4\pi$, so that the knottedness implies curviness... – Mariano Suárez-Alvarez♦ Mar 25 '10 at 5:15