Exotic aspherical manifolds

This lecture about exotic aspherical manifolds is dealing with the geometric realization of a simplicial complex, cubical cell complexes, the cubical complex PL, the universal cover of PL and the group WL and nonpositive curvatures. Another construction of PL and P-tildeL, the reflection group trick and aspherical manifolds not covered by Euclidean space are described. The Assembly Map Conjecture, aspherical manifolds which cannot be smoothed, an orientable and relative hyperbolization procedure and nontriangulable aspherical 4-manifolds are discussed