Mathematics and Statistics Faculty Publications
Title
Superinjective Simplicial Maps of Complexes of Curves and Injective Homomorphisms of Subgroups of Mapping Class Groups
Document Type
Article
Abstract
Let S be a closed, connected, orientable surface of genus at least 3, C(S) be the complex of curves on S and ModS∗ be the extended mapping class group of S. We prove that a simplicial map, λ:C(S)→C(S), preserves nondisjointness (i.e. if α and β are two vertices in C(S) and i(α,β)≠0, then i(λ(α),λ(β))≠0) iff it is induced by a homeomorphism of S. As a corollary, we prove that if K is a finite index subgroup of ModS∗ and f:K→ModS∗ is an injective homomorphism, then f is induced by a homeomorphism of S and f has a unique extension to an automorphism of ModS∗.
Repository Citation
Irmak, Elmas, "Superinjective Simplicial Maps of Complexes of Curves and Injective Homomorphisms of Subgroups of Mapping Class Groups" (2004). Mathematics and Statistics Faculty Publications. 58.
https://scholarworks.bgsu.edu/math_stat_pub/58
Publication Date
5-2004
Publication Title
Topology
Publisher
Elsevier
DOI
https://doi.org/10.1016/j.top.2003.03.002
Volume
43
Issue
3
Start Page No.
513
End Page No.
541