Asymptotic dimension of symmetric powers

Анотація

The main result of this note is the following one: asdim SPⁿ_GX ≤ n asdim X, where X is a proper metric space and asdim stands for the asymptotic dimension in the sense of Gromov. The corresponding resultis also valid for a generalization of the asymptotic dimension called the Assouad-Nagata asymptotic dimension. By SPⁿ_G the G-symmetric power functor is denoted.