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∗.

Publication Date

2004

Publication Title

Topology

Volume

43

Issue

3

Start Page No.

513

End Page No.

541

ISSN

0040-9383

DOI

10.1016/j.top.2003.03.002

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