Timeline for Can lens spaces be realized by surgery along torus links?
Current License: CC BY-SA 3.0
9 events
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| Jan 30, 2017 at 15:42 | answer | added | KeD | timeline score: 3 | |
| Sep 27, 2016 at 16:23 | comment | added | Franklin Wu | @MarcoGolla Thanks for answering. What I don't understand is an integral surgery along any $T(2,2q)$, even if $q\neq p$. | |
| Sep 27, 2016 at 7:55 | comment | added | Marco Golla | @magicker72: I think that you only get $S^3$ by doing (integral) surgeries along $\{*\}\times S^1$. In the 4-dimensional cobordism picture, you are attaching a 2-handle that cancels the 1-handle. However, if I'm not mistaken, the answer to the original question is yes; in fact, $L(p,1)$ is an integral surgery along any $T(2,2q)$, and this is a good exercise with handle diagrams. | |
| Sep 27, 2016 at 5:01 | comment | added | Franklin Wu | Exactly, a link on a Heegaard surface. By Lickorish’s theorem, any three-manifold $M$ can be obtained by surgery on a link $\mathbb{L}$ in $S^3$, thus in $S^2\times S^1$. While the Lens space $L(p,1)$ is homeomorphic to $S^3/\mathbb{Z}_p$. Thus I wish to set up a connection between $L(p,1)$ and $T(2,2p)$. @magicker72 | |
| Sep 27, 2016 at 4:50 | history | edited | Franklin Wu | CC BY-SA 3.0 |
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| Sep 27, 2016 at 0:46 | comment | added | magicker72 | Why are you focusing on a link? $S^3$ is surgery on $\{*\}\times S^1 \subset S^2 \times S^1$, and every $L(p, 1)$ is surgery on the same knot. | |
| Sep 27, 2016 at 0:41 | comment | added | magicker72 | By a torus link in $S^2 \times S^1$, do you mean a link sitting on a Heegaard surface? | |
| Sep 26, 2016 at 21:24 | review | First posts | |||
| Sep 26, 2016 at 21:36 | |||||
| Sep 26, 2016 at 21:22 | history | asked | Franklin Wu | CC BY-SA 3.0 |