Nilpotent class field theory for manifolds

Abstract

We introduce a nilpotent Hurewicz homomorphism for a topological manifold, following the Lie algebra method in nilpotent class field theory for local and number fields by H. Koch et al. Using Labute-Anick’s results on the determination of the Lie algebra attached to the lower central series of a group, we present explicitly nilpotent class field theory for some two and three dimensional manifolds.