Timeline for Integer surgery on $S^3$
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Apr 9, 2020 at 20:17 | comment | added | Mehdi Yazdi | Just to clarify, as Ryan mentioned, the above argument only shows that the diffeomorphism type of the resulting manifold is uniquely determined by the image of the meridian up to isotopy. | |
| Apr 9, 2020 at 12:43 | comment | added | Mehdi Yazdi | If we want to consider the case of compact, orientable 3-manifolds then the statement should be modified as follows: every compact orientable 3-manifold can be obtained by removing a regular neighborhood of some graph G in S^3 and integral surgery on a link L in S^3 - G. In any case, for the above argument we only need to consider a specific boundary component of M_1 which coincides with the boundary of B^3, and the argument is as before. | |
| Apr 9, 2020 at 12:40 | comment | added | Mehdi Yazdi | Assume for the moment that we are talking about closed orientable 3-manifolds. Then the boundaries of B^3 and M_1 coincide since after gluing them together along their boundary, we obtain a closed manifold. | |
| Apr 9, 2020 at 12:19 | vote | accept | Steve | ||
| Apr 9, 2020 at 12:19 | comment | added | Steve | Thank you but how do you know that $\partial M_1$ is a sphere? | |
| Apr 9, 2020 at 12:14 | vote | accept | Steve | ||
| Apr 9, 2020 at 12:19 | |||||
| Apr 9, 2020 at 12:02 | history | edited | Mehdi Yazdi | CC BY-SA 4.0 |
added 1 character in body
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| Apr 9, 2020 at 11:12 | history | answered | Mehdi Yazdi | CC BY-SA 4.0 |