Exotic aspherical 4-manifolds

Michael Davis; Kyle Hayden; Jingyin Huang; Daniel Ruberman; Nathan Sunukjian

doi:https://doi.org/10.4007/annals.2026.204.2.6

Exotic aspherical 4-manifolds

Pages 777-794 from Volume 204 (2026), Issue 2 by Michael Davis, Kyle Hayden, Jingyin Huang, Daniel Ruberman, Nathan Sunukjian

Abstract

We prove that there exist 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.

Keywords

4-manifolds, Borel conjecture, Coxeter groups, aspherical manifolds, exotic smooth structures

Mathematical Subject Classification

Primary 2020: 57R55 Secondary: 20F55

DOI

https://doi.org/10.4007/annals.2026.204.2.6

Milestones

Received: 10 December 2024
Revised: 6 January 2026
Accepted: 26 February 2026
Published online: 13 September 2026

Authors

Michael Davis

Department of Mathematics, The Ohio State University, Columbus, OH

Kyle Hayden

Department of Mathematics and Computer Science, Rutgers University-Newark, Newark, NJ

Jingyin Huang

Department of Mathematics, The Ohio State University, Columbus, OH

Daniel Ruberman

Department of Mathematics, Brandeis University, Waltham, MA

Nathan Sunukjian

Mathematics and Statistics Department, Calvin University, Grand Rapids, MI