Banach strong Novikov conjecture for polynomially contractible groups

Abstract

We prove the Banach strong Novikov conjecture for groups having polynomially bounded higher-order combinatorial functions. This includes all automatic groups.

v3: minor corrections, final version, to appear in Adv. Math. v2: corrected an error in the previous version (Lemma 2.9 in v1 had an erroneous proof) which led to a weakening of the main result