Resumen de A Hurewicz theorem for the Assouad�Nagata dimension

Nikolay Brodskiy, Jerzy Dydak , Michael Levin, Atish Mitra

• Given a function f : X Y of metric spaces, the classical Hurewicz theorem states that dim(X) dim(f) + dim(Y). We provide analogs of this theorem for the Assouad�Nagata dimension, asymptotic Assouad�Nagata dimension, and asymptotic dimension (the latter result generalizes a theorem of Bell and Dranishnikov). As an application, we estimate the asymptotic Assouad�Nagata dimension of a finitely generated group G in terms of the asymptotic Assouad�Nagata dimensions of the groups K and H from the exact sequence 1 K G H 1.