Borel conjectued aspherical closed manifolds are topologically rigid.(i.e.a homotopy equivalence between two aspherical manifolds is homotopic to a homeomorphism).
now,soppuse M is a K(G,1) space, it is well known that if G is a finite group,then M should be of infinite dimension.
I am not so comfortable with spaces of infinite dimesion. are there some good (natural) prespective in viewing such spaces.