Timeline for why is there such a 1-form on a planar open book?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 18, 2015 at 14:18 | comment | added | Ken Baker | Any map dual to a Seifert surface for $L'$. They just ask that the preimage of a regular value is a Seifert surface. | |
| Jan 16, 2015 at 16:57 | comment | added | nikita | I see what you are saying, but then what could be the map $\sigma: S^3-L'\to S^1$ they are talking about? | |
| Jan 15, 2015 at 14:46 | comment | added | Ken Baker | The link $L'$ in $S^3$ (the surgery dual of the link $L$ in $Y$) is not necessarily a fibered link. If the knot $K$ is the remaining component of the binding $B$ in $Y$, then after surgery on $L$, in $S^3$ we see that $L'$ is a closed pure braid with $K$ as a braid axis. Generically a link that is the closure of a pure braid is not fibered. But Gay and Stipsicz do not claim $L'$ is fibered. From a glance, it appears that the function of $S^3$ here is that it is a homology sphere so that $L'$ will be null-homologous. | |
| Jan 15, 2015 at 1:53 | history | asked | nikita | CC BY-SA 3.0 |