Abstract: The Borel conjecture asserts that closed aspherical manifolds are determined up to homeomorphism by their fundamental groups. The general conjecture is still open, but it has been proved for classes of manifolds satisfying certain geometric properties. Using surgery theory in dimension three and stabilizing, we show that the assertion holds for new classes of manifolds, and we also discuss the possibilities of counterexamples to Borel's conjecture. This is joint work with Slawomir Kwasik, Tulane University.