Exotic aspherical 4-manifolds

TL;DR

This paper constructs exotic aspherical smooth 4-manifolds that are homeomorphic but not diffeomorphic, providing counterexamples to a smooth Borel conjecture analog in four dimensions.

Contribution

It introduces a novel application of the reflection group trick to produce exotic 4-manifolds with specific topological properties.

Findings

Constructed closed, aspherical 4-manifolds that are homeomorphic but not diffeomorphic.

Provided counterexamples to the smooth Borel conjecture in dimension four.

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.