Injections of Artin groups

2005/01/04 by Robert W. Bell, Dan Margalit, Bell, Robert W. +1
Mathematics · #20F36 #57M07 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0501051

openalex publication_date 2005/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Automorphisms of surface braid groups
• Complexes of Nonseparating Curves and Mapping Class Groups

Related

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• Right-angled Artin groups and a generalized isomorphism problem for\n finitely generated subgroups of mapping class groups
• Braid groups are almost co-Hopfian
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• On the Subgroups of Right Angled Artin Groups and Mapping Class Groups