Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
up vote 2 down vote accepted

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.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.