Timeline for Reducible 3d torus bundles
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 14, 2009 at 2:08 | comment | added | Ryan Budney | No. There's also reducible elements, things like $\begin{pmatrix} 1 & 0 \\ n & 1\end{pmatrix}$ for $n \neq 0$. | |
| Dec 8, 2009 at 21:52 | comment | added | janmarqz | there are only 5 periodic elements in SL_2(Z) right? so the remaining are pA? | |
| Dec 8, 2009 at 21:46 | comment | added | Sam Nead | They are called Anosov maps when the surface in question is the two-torus. They are exactly the elements of SL(2, Z) having an eigenvalue greater than one. Perhaps you would be interested in the relevant Wikipedia page: en.wikipedia.org/wiki/Torus_bundle | |
| Dec 8, 2009 at 21:41 | comment | added | janmarqz | Maybe if we could see an algebraic condition for pseudo Anosov bundles... | |
| Dec 8, 2009 at 21:40 | comment | added | Sam Nead | I also believe that this will work. Another much more machine dependent proof would go through the Nielsen-Thurston classification of mapping classes and our previous discussion (on this website!) of the classification of periodic mappings of the two-torus. | |
| Dec 8, 2009 at 21:38 | comment | added | janmarqz | Prof Wilton: do you know that there are only seven periodic elements? | |
| Dec 8, 2009 at 21:18 | history | answered | HJRW | CC BY-SA 2.5 |