10
$\begingroup$

I have questions about Akbulut and Kirby's paper Mazur manifolds.

I couldn't figure out the following equality passages:

Figure 23

Figure 23

Any help will be appreciated.

$\endgroup$
  • $\begingroup$ Rolfsen's book: Knots and Links especially section 9H is a good resource for working through examples like this. Granted this section does rely on previous sections especially the linking number section, but that can be useful background too. $\endgroup$ – Neil Hoffman Feb 10 at 22:03
9
$\begingroup$

enter image description here

Here is a proof with pictures. Observe that blowing up and blowing own doesn't change the 3 manifold,i.e, the boundary. So all these above pictures have same boundary. As a 3 manifolds all of these are isomorphic.

| cite | improve this answer | |
$\endgroup$

Your Answer

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