1
$\begingroup$

Is it true that for even dimensional differentiable manifold $M^{2n}$ all singular homology classes in dimension less than $n$ can be represented by a submanifold?

$\endgroup$
  • 5
    $\begingroup$ Look at the two answers to this duplicate question:mathoverflow.net/questions/21171/… $\endgroup$ – Achim Krause Mar 12 '15 at 0:02
  • 3
    $\begingroup$ In particular, there are obstructions for an integral homology class to be represented by a manifold map altogether (you can get some odd multiple in general), but as soon as that part works you can turn such a map into an embedding in the dimensions you're asking for. $\endgroup$ – Achim Krause Mar 12 '15 at 0:04

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.