Proof of Theorem I.38

Abstract

The rest of the lecture notes will be devoted to a proof of Theorem I.38. Right from the beginning the proof will bifurcate into two cases: the contact manifold B is 3-dimensional and dim B > 3. If dimB = 3 we will argue directly using slices that the orbit spaceB/Gis homeomorphic to a closed interval [0, 1] and then use this to compute the integral cohomology ofB. This will show that B cannot be homeomorphic to $S^* \mathbb{T}^2 = \mathbb{T}^3$