Exotic aspherical 4-manifolds

Abstract

We construct closed, aspherical, smooth 4-manifolds that are homeomorphic but not diffeomorphic. These provide counterexamples to a smooth analog of the Borel conjecture in dimension four. Our technique is to apply the `reflection group trick' of the first author to pairs of exotic 4-manifolds with boundary constructed by the second author and Piccirillo.

14 pages, 3 figures. Second version corrects some introductory remarks. Final version; to appear in Annals of Mathematics