Mis said to be aspherical if its universal covering space is contractible. Farrell and Hsiang have conjectured : Conjecture A.(Topological rigidity of aspherical manifolds.) Any homotopy equivalence f: N → Mbetween closed aspherical manifolds is homotopic to a homeomorphism,
and its analogue in algebraic
K-theory: Conjecture B. The Whitehead groups Whj(π1 M)(j≥ 0) of the fundamental group of a closed aspherical manifold Mvanish.