A Homological Finiteness Criterion.
The present paper is a continuation of our previous paper [Topology 44 (2005), 747-767], where we extended the Burau representation to oriented tangles. We now study further properties of this construction.
The purpose of this paper is to prove the existence of a free subgroup of the group of all affine transformations on the plane with determinant 1 such that the action of the subgroup is locally commutative.