Timeline for A special ribbon graph presents a cylinder.
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 19, 2012 at 6:15 | vote | accept | knot | ||
| Feb 19, 2012 at 6:14 | vote | accept | knot | ||
| Feb 19, 2012 at 6:15 | |||||
| Feb 13, 2012 at 8:11 | comment | added | knot | I reduced this question to the new question mathoverflow.net/questions/88334. Could you take a look at it and if you have time to write answer, please do so. Thanks. | |
| Feb 10, 2012 at 17:19 | comment | added | Kevin Walker | I don't have a detailed answer for your question about parameterizations, but in general you want to identify annuli of the form (curve)$\times I$ in $\Sigma\times I$ (such as the one in Turaev's Figure 2.5) and then use these annuli to construct an identification between pants decompositions of the two boundary components of $\Sigma\times I$. | |
| Feb 10, 2012 at 5:48 | comment | added | knot | Thank you for the answer. I took a look at Rolfsen and I think I understand the result of the surgery is the cylinder $\Sigma \times I$. But I don't see the parametrization of the upper boundary is the identity. By the construction, the top parametrization is the compositon of mir and $f^+: -R_{t^+} \rightarrow \Sigma^+ $ (by the book's notation on p.159 & 168). How does the surgery affect the parametrization? I guess we need one more mir to have the identity parametrization. | |
| Feb 5, 2012 at 14:39 | history | answered | Kevin Walker | CC BY-SA 3.0 |