Superinjective Simplicial Maps of Complexes of Curves and Injective Homomorphisms of Subgroups of Mapping Class Groups II
| dc.creator | Irmak, Elmas | |
| dc.date | 2003-11-23 | |
| dc.date | 2003-12-29 | |
| dc.date.accessioned | 2026-07-07T05:03:11Z | |
| dc.date.available | 2026-07-07T05:03:11Z | |
| dc.description | Let R be a compact, connected, orientable surface of genus g with p boundary components. Let C(R) be the complex of curves on R and Mod_R^* be the extended mapping class group of R. Suppose that either g = 2 and p > 1 or g > 2 and p >= 0. We prove that a simplicial map lambda from C(R) to C(R) is superinjective if and only if it is induced by a homeomorphism of R. As a corollary, we prove that if K is a finite index subgroup of Mod_R^* and f is an injective homomorphism from K to Mod_R^*, then f is induced by a homeomorphism of R and f has a unique extension to an automorphism of Mod_R^*. This extends the author's previous results about closed connected orientable surfaces of genus at least 3, to the surface R. | |
| dc.description | 37 pages, 19 figures; The proof for surfaces of genus two with at least two boundary components is added | |
| dc.identifier | https://arxiv.org/abs/math/0311407 | |
| dc.identifier | http://arxiv.org/abs/math/0311407 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69314 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M99 (Primary), 20F38 (Secondary) | |
| dc.title | Superinjective Simplicial Maps of Complexes of Curves and Injective Homomorphisms of Subgroups of Mapping Class Groups II | |
| dc.type | text |