Timeline for Fixed points of IA automorphisms
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 16, 2014 at 17:52 | vote | accept | Mark Grant | ||
| Aug 3, 2013 at 15:34 | answer | added | Lee Mosher | timeline score: 3 | |
| Aug 2, 2013 at 9:26 | comment | added | HJRW | @LeeMosher, perhaps you should post your comment as an answer? | |
| Aug 1, 2013 at 6:23 | comment | added | Mark Grant | Thanks everyone. I didn't realize the close connection with the Torelli group. | |
| Jul 31, 2013 at 22:02 | comment | added | Lee Mosher | You can construct examples with no fixed elements at all, out of the examples mentioned by Misha. Let $S$ be of genus $g$ with $1$ boundary component, consider two isomorphisms from $\pi_1(S)$ to $F_n$ taking the boundary component to two nonconjugate elements, push forward two Torelli pseudo-Anosov mapping classes on $S$ under these two isomorphisms respectively to get two $IA_n$ automorphisms of $F_n$ fixing different conjugacy classes, then multiply high powers of those automorphisms together. The resulting $IA_n$ automorphism will fix no conjugacy classes at all. | |
| Jul 31, 2013 at 15:32 | comment | added | Misha | As Mark says, just take a pseudo-Anosov homeomorphism of a genus g surface with 1 boundary component which lies in Torelli subgroup. Then, even up to conjugation, only the peripheral elements are fixed, and they are in the commutator subgroup. | |
| Jul 31, 2013 at 14:34 | comment | added | user6976 | Did you look at elements of the Torelli subgroup for a punctured surface? | |
| Jul 31, 2013 at 14:28 | comment | added | Mark Grant | @MarkSapir Wishful thinking, mostly. I am interested in any information or references regarding IA automorphisms of free groups. | |
| Jul 31, 2013 at 14:19 | comment | added | user6976 | Why do you think it might be true for $n\ge 3$? | |
| Jul 31, 2013 at 14:10 | history | asked | Mark Grant | CC BY-SA 3.0 |