Timeline for extension of surface homeomorphism
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 12, 2012 at 21:07 | history | edited | Ian Agol | CC BY-SA 3.0 |
added 281 characters in body
|
| Jun 2, 2012 at 20:22 | comment | added | Sam Nead | Arrange matters so that $g$ doesn't send $\lambda^+(f)$ to $\lambda^-(f)$; post-compose $g$ with a separating Dehn twist if necessary. Now use the Brouwer fixed point theorem and the north-south dynamics of $f$ to prove (for $n$ sufficiently large) that the action of $f^n \circ g$ has exactly two fixed points: one close to $\lambda^+(f)$ and one close to $g^{-1}(\lambda^-(f))$. | |
| Jun 2, 2012 at 19:24 | comment | added | Igor Rivin | @Sam: why is that? | |
| Jun 2, 2012 at 17:18 | comment | added | Sam Nead | Igor - take any pA element $f$ that acts trivially on homology. Take any $g$ with the desired action on homology. Then for some $n$ the element $f^n \circ g$ will be pA. | |
| Jun 2, 2012 at 15:57 | comment | added | Igor Rivin | Why does one have a pseudo-ANosov giving any symplectic matrix? | |
| Jun 2, 2012 at 15:11 | history | answered | Ian Agol | CC BY-SA 3.0 |