Injections of Artin groups

26Citations
Citations of this article
9Readers
Mendeley users who have this article in their library.

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 given by a homeomorphism of a punctured sphere together with a map to the integers. The technique, following Ivanov, is to prove that every superinjective map of the curve complex of a sphere with at least 5 punctures is induced by a homeomorphism. We also determine the automorphism group of the pure braid group on at least 4 strands. © Swiss Mathematical Society.

References Powered by Scopus

Abelian and solvable subgroups of the mapping class group

147Citations
N/AReaders
Get full text

On the residual finiteness of certain mapping class groups

116Citations
N/AReaders
Get full text

Automorphisms of the complex of curves

110Citations
N/AReaders
Get full text

Cited by Powered by Scopus

Pullback invariants of thurston maps

16Citations
N/AReaders
Get full text

Automorphisms of the Torelli complex and the complex of separating curves

12Citations
N/AReaders
Get full text

Automorphisms of curve complexes on nonorientable surfaces

11Citations
N/AReaders
Get full text

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Cite

CITATION STYLE

APA

Bell, R. W., & Margalit, D. (2007). Injections of Artin groups. Commentarii Mathematici Helvetici, 82(4), 725–751. https://doi.org/10.4171/CMH/108

Readers' Seniority

Tooltip

PhD / Post grad / Masters / Doc 4

44%

Professor / Associate Prof. 3

33%

Researcher 2

22%

Readers' Discipline

Tooltip

Mathematics 9

100%

Save time finding and organizing research with Mendeley

Sign up for free