Rank gradient and cost of Artin groups and their relatives
Aditi Kar
University of Southampton, UKNikolay Nikolov
University of Oxford, UK
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Abstract
We prove that the rank gradient vanishes for mapping class groups of genus greater than , for all , , and any Artin group whose underlying graph is connected. These groups have fixed price . We compute the rank gradient and verify that it is equal to the first -Betti number for some classes of Coxeter groups.
Cite this article
Aditi Kar, Nikolay Nikolov, Rank gradient and cost of Artin groups and their relatives. Groups Geom. Dyn. 8 (2014), no. 4, pp. 1195–1205
DOI 10.4171/GGD/300