Rank gradient and cost of Artin groups and their relatives

Aditi Kar; Nikolay Nikolov

Rank gradient and cost of Artin groups and their relatives

Group Theory 2014-05-06 v4

Authors: Aditi Kar , Nikolay Nikolov

Abstract

We prove that the rank gradient vanishes for mapping class groups of genus bigger than 1, $Aut(F_n)$ , for all $n$ , $Out(F_n)$ for $n \geq 3$ , 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 mapping class groups Aut(F_n) Out(F_n) Coxeter groups L^2-Betti number

Cite

@article{arxiv.1210.2873,
  title  = {Rank gradient and cost of Artin groups and their relatives},
  author = {Aditi Kar and Nikolay Nikolov},
  journal= {arXiv preprint arXiv:1210.2873},
  year   = {2014}
}

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