Is h-cobordism theorem true on smooth category?

On h-coobrdism page of Wikipedia, it says that h-cobordism theory is true for smooth category. As far as I know, it would imply that smooth Poincare conjecture is true for dimension greater than 6, which is not true by milnor. Is the Wikipedia page is wrong or am I doing something wrong?

-
add comment

1 Answer

The smooth h-cobordism Theorem is true. If you want to prove the high dimensional Poincaré conjecture, at some time you will cut out discs in your homotopy sphere and apply the h-cobordism theorem. But then you have to extend some diffeo from the boundary of the disc to the whole disc, which can be made continuously through a cone construction but not smoothly. Hope that helps.

-
add comment