On pp. 166 of Scorpan's "The Wild World of 4--manifolds", he gives an example of a parallelizable 4-manifold ($S^1\times S^3$) and then asserts: "there are no simply connected examples". It's confusing to me whether he means that there are no such examples in general, or examples that are 4-manifolds. In any case, here is my question:
Do there exist (compact, smooth, oriented) simply connected manifolds that are parallelizable? 4-manifolds?
(Recall that a manifold is called parallelizable if it has a trivial tangent bundle.)