Counting maps from a surface to a graph
| dc.creator | Bestvina, Mladen | |
| dc.creator | Feighn, Mark | |
| dc.date | 2005-05-17 | |
| dc.date.accessioned | 2026-07-07T05:19:58Z | |
| dc.date.available | 2026-07-07T05:19:58Z | |
| dc.description | Let F be a non-abelian finite rank free group, and let H_g be the fundamental group of a surface of genus g with one boundary component represented by D_g in H_g. So, H_g is the free group <a_1,b_1,...,a_g,b_g> and D_g is the product of commutators [a_1,b_1]...[a_g,b_g]. Given x in F, we are interested in the number num(x) of primitive, i.e. root-free, images of monomorphisms (H_g,D_g) -> (F,x). Our main result is that f(g) >= 2^g where f(g)=sup num(x), where sup is taken over all elements x in F. This answers a question of Zlil Sela that is related to his work on the Tarski problem. We also show that f is independent of F and go on to obtain similar results where the monomorphisms considered are additionally required to have minimal genus. | |
| dc.identifier | https://arxiv.org/abs/math/0505363 | |
| dc.identifier | http://arxiv.org/abs/math/0505363 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75220 | |
| dc.subject | Geometric Topology | |
| dc.subject | Group Theory | |
| dc.title | Counting maps from a surface to a graph | |
| dc.type | text |