A manifold M is 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 → M between closed aspherical manifolds is homotopic to a homeomorphism,
and its analogue in algebraic K-theory:
Conjecture B. The Whitehead groups Whj(π1M)(j ≥ 0) of the fundamental group of a closed aspherical manifold M vanish.
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