An etale approach to the Novikov conjecture

We show that the rational Novikov conjecture for a group $\mathrm{\Gamma }$ of finite homological type follows from the mod 2 acyclicity of the Higson compactifcation of an E$\mathrm{\Gamma }$. We then show that for groups of finite asymptotic dimension the Higson compactification is mod p acyclic for all p, and deduce the integral Novikov conjecture for these groups.