Rank gradient and cost of Artin groups and their relatives
Rank gradient and cost of Artin groups and their relatives
We prove that the rank gradient vanishes for mapping class groups of genus greater than 1 , \mathrm{Aut}(F_n) for all n , \mathrm{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 …