Timeline for Parabolic elements and hyperbolic elements in SL(2,R)
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 24 at 20:21 | comment | added | Sam Nead | @Dinisaur - In dimension three the argument is extremely similar (including the "shapes" of the matrices). | |
| Feb 24 at 18:10 | comment | added | Dinisaur | Is it possible to give a similarly elementary argument to prove the same statement in dim>2? | |
| Aug 9, 2022 at 20:10 | comment | added | Sam Nead | Yes, some pA maps arise in this way. In particular, if you have a flat surface that decomposes nicely (in two ways) as a union of annuli with rationally related moduli, then the right twist (aka shear) on one, followed by the left twist on the other, will be pA. The Thurston--Veech construction is usually phrased as a special case of this, where the flat surface is tiled by squares. | |
| Aug 9, 2022 at 19:59 | comment | added | John Rached | I see. But you can produce pA diffeomorphisms from a product of two transverse parabolic elements, using the Thurston-Veech construction, correct ? | |
| Aug 9, 2022 at 18:34 | comment | added | Sam Nead | It is not true that all pA maps arise from the Thurston-Veech construction. See arxiv.org/abs/1410.6974 | |
| Aug 9, 2022 at 13:23 | comment | added | John Rached | Great, I was wanting something like this, as pseudo-Anosov diffeomorphisms have derivatives with trace larger than 2, and you can produce any one of these (Thurston) from a product of parabolic elements | |
| Aug 9, 2022 at 13:14 | vote | accept | John Rached | ||
| Aug 9, 2022 at 8:29 | history | edited | Sam Nead | CC BY-SA 4.0 |
third proof
|
| Aug 9, 2022 at 8:23 | history | answered | Sam Nead | CC BY-SA 4.0 |