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.
Asked
Active
Viewed 97 times
4
-
For anyone looking for this statement, it is an exercise at the end of section 1 of chapter VI. – Michael Albanese Jul 14 '17 at 15:01