Groups, Geometry, and Dynamics
Full-Text PDF (148 KB) | Metadata | Table of Contents | GGD summary
Published online: 2014-12-31
Rank gradient and cost of Artin groups and their relativesAditi Kar and Nikolay Nikolov (1) University of Southampton, UK
(2) University of Oxford, UK
We prove that the rank gradient vanishes for mapping class groups of genus greater than 1, Aut($F_n$) for all $n$, Out($F_n$), $n≥3$ and any Artin group whose underlying graph is connected. These groups have fixed price 1. We compute the rank gradient and verify that it is equal to the first $L^2$-Betti number for some classes of Coxeter groups.
Keywords: Rank gradient, cost, Artin groups
Kar Aditi, Nikolov Nikolay: Rank gradient and cost of Artin groups and their relatives. Groups Geom. Dyn. 8 (2014), 1195-1205. doi: 10.4171/GGD/300