Rank gradient and cost of Artin groups and their relatives

  • Aditi Kar

    University of Southampton, UK
  • Nikolay Nikolov

    University of Oxford, UK

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