Injections of Artin groups
Group Theory
2007-05-23 v2 Geometric Topology
Abstract
We study those Artin groups which, modulo their centers, are finite index subgroups of the mapping class group of a sphere with at least 5 punctures. In particular, we show that any injective homomorphism between these groups is parameterized by a homeomorphism of a punctured sphere together with a map to the integers. We also give a generating set for the automorphism group of the pure braid group on at least 4 strands. The technique, following Ivanov, is to prove that every superinjective map of the complex of curves of a sphere with at least 5 punctures is induced by a homeomorphism.
Keywords
Cite
@article{arxiv.math/0501051,
title = {Injections of Artin groups},
author = {Robert W. Bell and Dan Margalit},
journal= {arXiv preprint arXiv:math/0501051},
year = {2007}
}
Comments
21 pages, 8 figures, some corrections, new sections