Timeline for Equivalence of surjections from a surface group to a free group
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 18, 2018 at 2:05 | vote | accept | user101010 | ||
| Oct 15, 2018 at 8:15 | comment | added | YCor | For context, there's no homomorphism onto $F_{g+1}$. Out of curiosity, what can be said of the set of surjective homomorphisms $\pi_1(S)\to F_k$ modulo $Aut(\pi_1(S))\times Aut(F_k)$, when $1\le k<g$? is it infinite? | |
| Oct 15, 2018 at 5:42 | answer | added | Jean Raimbault | timeline score: 9 | |
| Oct 15, 2018 at 2:03 | comment | added | PseudoNeo | Oh, thank you, I was misreading the question (I mixed up $F_g$ and $F_{2g}$) and was very confused. | |
| Oct 15, 2018 at 2:02 | comment | added | mme | @PseudoNeo Algebraically, yes: kill all of the $b_i$. Geometrically, yes: the surface is the boundary of a handlebody, equivalent to a wedge of $g$ circles. | |
| Oct 15, 2018 at 2:00 | comment | added | PseudoNeo | A naive question: is it clear such a surjection exists? | |
| Oct 15, 2018 at 0:41 | history | asked | user101010 | CC BY-SA 4.0 |