Homomorphisms from automorphism groups of free groups
| dc.creator | Bridson, Martin R | |
| dc.creator | Vogtmann, Karen | |
| dc.date | 2002-09-16 | |
| dc.date.accessioned | 2026-07-07T04:50:54Z | |
| dc.date.available | 2026-07-07T04:50:54Z | |
| dc.description | The automorphism group of a finitely generated free group is the normal closure of a single element of order 2. If $m$ is less than $n$ then a homomorphism $Aut(F_n)\to Aut(F_m)$ can have cardinality at most 2. More generally, this is true of homomorphisms from $\Aut(F_n)$ to any group that does not contain an isomorphic copy of the symmetric group $S_{n+1}$. Strong constraints are also obtained on maps to groups that do not contain a copy of $W_n= (\Bbb Z/2)^n\rtimes S_n$, or of $\Bbb Z^{n-1}$. These results place constraints on how $\Aut(F_n)$ can act. For example, if $n\ge 3$ then any action of $\Aut(F_n)$ on the circle (by homeomorphisms) factors through $\text{\rm{det}}:Aut(F_n) \to \Bbb Z_2$ . | |
| dc.description | 10 Pages, to appear in J. London Math. Soc | |
| dc.identifier | https://arxiv.org/abs/math/0209191 | |
| dc.identifier | http://arxiv.org/abs/math/0209191 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64958 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | 20F65, 20F28 | |
| dc.title | Homomorphisms from automorphism groups of free groups | |
| dc.type | text |