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

The book Differential Manifolds by Kosinski claimed we can embed the connected sum of two submanifolds of codimension $>1$ into the ambient manifold. I am wondering why we need the extra condition $>1$ at here. At least in dimension 1-3 I could not find a counter example. On the other hand I also do not know how to prove this rigorously enough. So I venture to ask.

share|cite|improve this question

Your Answer


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

Browse other questions tagged or ask your own question.