3
$\begingroup$

Suppose I keep in my pocket a manifold with boundary $M$ , and I provide you access to $int M := M \setminus \partial M$ up to homeomorphism/diffeomorphism. What can you deduce about $\partial M$? can you reconstruct it up to homotopy/homeomorphism/diffeomorphism? can you deduce homotopical / topologial / smooth invariants of it?

Improve this question
$\endgroup$
4
  • 4
    $\begingroup$ Did you want to say that $M$ is compact? $\endgroup$
    – Anton Petrunin
    Jun 19, 2016 at 20:55
  • 1
    $\begingroup$ Consider closed interval $[0,1]$. It's interior is topologically equivalent to the real line. $\endgroup$
    – Vít Tuček
    Jun 19, 2016 at 20:59
  • 2
    $\begingroup$ Adding boundaries to open manifolds has been discussed at least in these previous questions: 22441, 34602, 81714, 83356, 158391. So in a sense this is a duplicate. $\endgroup$
    – Igor Khavkine
    Jun 19, 2016 at 21:02
  • 6
    $\begingroup$ This is basically the same as the following previous question: mathoverflow.net/q/81714/317 $\endgroup$
    – Andy Putman
    Jun 19, 2016 at 21:06

0

Reset to default