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Rank gradient and cost of Artin groups and their relatives

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 نشر من قبل Aditi Kar
 تاريخ النشر 2012
  مجال البحث
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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.



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