Exotic aspherical 4-manifolds
Geometric Topology
2026-05-06 v3 Algebraic Topology
Group Theory
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.
Keywords
Cite
@article{arxiv.2411.19400,
title = {Exotic aspherical 4-manifolds},
author = {Michael Davis and Kyle Hayden and Jingyin Huang and Daniel Ruberman and Nathan Sunukjian},
journal= {arXiv preprint arXiv:2411.19400},
year = {2026}
}
Comments
14 pages, 3 figures. Second version corrects some introductory remarks. Final version; to appear in Annals of Mathematics