On dimension growth of groups

نویسندگان

  • Alexander DRANISHNIKOV
  • Mark SAPIR
  • ALEXANDER DRANISHNIKOV
  • MARK SAPIR
چکیده

The (asymptotic) dimension growth functions of groups were introduced by Gromov in 1999. In this paper, we show connections between dimension growth and expansion properties of graphs, Ramsey theory and the Kolmogorov-Ostrand dimension of groups and prove that all solvable subgroups of the R.Thompson group F have polynomial dimension growth. We introduce controlled dimension growth function and prove that the exponentially controlled dimension growth is exponential for the Thompson group F and some solvable of class 3 groups. The paper contains many open questions.

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تاریخ انتشار 2012