Timeline for A doubt from "Geometry of the complex of curves II: Hierarchical structure" by Masur and Minsky
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 1, 2014 at 10:56 | comment | added | Cusp | Exactly. That's what I have realized from your comment. I was actually missing this point. Thanks again. | |
| May 1, 2014 at 10:54 | comment | added | Sam Nead | You have to use some geometric notion to track projections to annular domains, because annuli don't have enough topology. | |
| May 1, 2014 at 10:54 | comment | added | Cusp | Its okay. I knew that result. | |
| May 1, 2014 at 10:53 | comment | added | Sam Nead | Perhaps I should have said "It is a non-trivial exercise..." | |
| May 1, 2014 at 10:53 | comment | added | Cusp | Again thanks. Actually I was trying to understand this from a complete topological background, so I was trying to avoid any use of geometry. | |
| May 1, 2014 at 10:47 | comment | added | Sam Nead | You can do things this way. However, taking the Gromov closure only requires that the metric space in question be $\delta$-hyperbolic. It is an exercise to check that for any metric $\rho$ on $S$ (with $\chi(S) < 0$) the annular cover is $\delta$-hyperbolic. (However, it is true that $\delta$ depends $\rho$.) | |
| May 1, 2014 at 10:43 | vote | accept | Cusp | ||
| May 1, 2014 at 10:42 | comment | added | Cusp | Thank you very much for the clarification. But I am still confused about the third part. The Gromov clouser requires the cover to have a negatively curved metric right! So are we considering $\bar{Y}$ as a quotient of $\mathbb{H}^2?$ because then it is same as considering a hyperbolic metric in $S$. | |
| May 1, 2014 at 10:24 | history | answered | Sam Nead | CC BY-SA 3.0 |