Complexes of Nonseparating Curves and Mapping Class Groups
| dc.creator | Irmak, Elmas | |
| dc.date | 2004-07-16 | |
| dc.date | 2004-08-05 | |
| dc.date.accessioned | 2026-07-07T05:10:23Z | |
| dc.date.available | 2026-07-07T05:10:23Z | |
| dc.description | Let $R$ be a compact, connected, orientable surface of genus $g$, $Mod_R^*$ be the extended mapping class group of $R$, $\mathcal{C}(R)$ be the complex of curves on $R$, and $\mathcal{N}(R)$ be the complex of nonseparating curves on $R$. We prove that if $g \geq 2$ and $R$ has at most $g-1$ boundary components, then a simplicial map $λ: \mathcal{N}(R) \to \mathcal{N}(R)$ is superinjective if and only if it is induced by a homeomorphism of $R$. We prove that if $g \geq 2$ and $R$ is not a closed surface of genus two then $Aut(\mathcal{N}(R))= Mod_R^*$, and if $R$ is a closed surface of genus two then $Aut(\mathcal{N}(R))= Mod_R ^* /\mathcal{C}(Mod_R^*)$. We also prove that if $g=2$ and $R$ has at most one boundary component, then a simplicial map $λ: \mathcal{C}(R) \to \mathcal{C}(R)$ is superinjective if and only if it is induced by a homeomorphism of $R$. As a corollary we prove some new results about injective homomorphisms from finite index subgroups to $Mod_R^*$. The last two results complete the author's previous results to connected orientable surfaces of genus at least two. | |
| dc.description | 24 pages, 13 figures; The result about automorphism group of complex of nonseparating curves has been extended to compact, connected, orientable surfaces of genus at least two | |
| dc.identifier | https://arxiv.org/abs/math/0407285 | |
| dc.identifier | http://arxiv.org/abs/math/0407285 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71915 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M99; 20F38 | |
| dc.title | Complexes of Nonseparating Curves and Mapping Class Groups | |
| dc.type | text |